e algebraiese breuke
TRANSCRIPT
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Faktorisering….
Verskil van
vierkante?
Groepeer
Gemeenskaplike faktor(e)
2-Term 3-Term Meer terme
Som / Verskil van derdemagte?
)1( +=+ab
bab
))((
22
baba
ba
+−=−
( )( )
))(( 22
33
yxyxyx
yx
+−+=+
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ONTHOU!
Probeer altyd breuke so ver moontlik vereenvoudig
deur uit te kanselleer.
Ons mag nie uitkanselleer OOR ‘n ‘+’ of ‘-’ nie,
dus faktoriseer eers
(Soortgelyk aan faktorisering by eksponente).
STAPPE:
→ Faktoriseer → Kanselleer uit → Vereenvoudig
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VOORBEELD 1:
a
aa
6
63 2 +a
aa
6
)2(3 +=Faktoriseer tellers & noemers:
2
)2( += aKanselleer uit:
L.W: 2 mag nie indeel in hakie se 2 nie, want die hakie vorm ‘n eenheid!
a ≠ 0
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VOORBEELD 2:
)2(
)2(3)1)(2(
−−++−
x
xxx Faktoriseer tellers & noemers:
Kanselleer uit:
)2(
]3)1)[(2(
−++−=
x
xx
4
]3)1[(
+=++=
x
x
x ≠ 2
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VOORBEELD 3:
x
xx
3
36 2 + Faktoriseer tellers & noemers:
Kanselleer uit:
x
xx
3
)12(3 +=
12 += x
x ≠ 0
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VOORBEELD 4:
2
24
−− x Faktoriseer tellers &
noemers:
Kanselleer uit:
2
)2(2
−+−−= x
2
)2(
−=+−=
x
x
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HUISWER
K
OEF 5.28 Nr 9 - 18
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9.
x
xx
2
42 2 −
x
xx
2
)2(2 −=
2−= x
Faktoriseer
Kanselleer
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Oef 5.28
10.2
32
3
63
x
xx −
2
2
3
)21(3
x
xx −=
x21−=
Faktoriseer
Kanselleer
11.2
2222
2
24
y
yzyx +
2
222
2
)12(2
y
zxy +=
12 22 += zx
Faktoriseer
Kanselleer
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Oef 5.28
12.
7
721 x−−
7
)3(7 x−−=
x−−= 3
13.
a
aa
2
22 +
a
aa
2
)2( +=
2
2+= a
14.
)1(
)2)(1(
+−+
x
xx
2−= x
15.1
)1()2)(1(
+++−+
x
xxx
)1(
)12)(1(
++−+=
x
xx
= x - 1
)1(
)2)(1(
+−+
x
xx
16.
)2(
)2(3)2(
++−+
a
aaa
a31−=
17.
)2(
)31)(2(
+−+
a
aa
)1(
)1()1(2 2
++++
a
aa
)1(
)1)1(2)(1(
++++=
a
aa
= 2a + 3
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Oef 5.28
18.
x
xx
6
63 2 +
x
xx
6
)2(3 +=2
2
2+= x
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Vermenigvuldig breuke
Stap 1: Vereenvoudig deur uit te kanselleer (maak breuke kleiner)
Stap 2: Bereken: teller x teller
noemer x noemer
8
9
15
2 ×3
5
1
4
45
31
××=
20
3=
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Deel breuke
DEEL (Maal met resiprook):
Stap 1: Verander deelteken na maalteken.
Stap 2: Ruil die breuk NA die deelteken se
teller en noemer om.
Stap 3: Maal breuke soos voorheen.
8
6
15
3 ÷−
6
8
15
3×−=
35
41
××−=
15
4−=
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Vir algebraiese breuke (X en ÷)
3
2
2
2
4
)1(22
12
1
x
x
x
x
xx
x +÷−×+−
−
)1)(1(
4)1(2
)1)(1(
)1)(1( 3
++×−×
−−−+=
xx
x
x
x
xx
xx x²
)1(
8 2
+=x
x
Vermenigvuldig
Faktoriseer
tellers & noemers
Kanselleer uit
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HUISWER
K
OEF 5.29 Nr 1, 2, 4, 6, 8, 9, 11
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Oef 5.29
21
4
2
7 2x
x×1.
21
4
2
7 2x
x×=
3
2x
3
2x=
42
3 xx ÷2.
2
x
x 4
2
3 ×=
6=
s
r
r
s
s
r 2
2
3 46
3
2 ÷×4.
2
1=
22
3
4
6
3
2
r
s
r
s
s
r ××=
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Oef 5.29
8.)163
8(
3
23
3
3
2
a
b
b
a
b
a ×÷
2
b
4=
a²)
163
8(
3
23
3
3
2
a
b
b
a
b
a ×÷=b²
2
2
3
2
63
2
b
a
b
a ÷=
2
2
3
2 6
3
2
a
b
b
a ×=
b
2
6.)(
4
9
422 qpqp
qp
q
p
+÷−×
4
)(
9
4 2
2
qpq
p
qp
q
p +×−×=
9
))(( qpqp +−=
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Oef 5.29
9.
x
x
x
x
10
1
5
12 −÷−
)1x(
x10
x5
)1x)(1x(
−×−+=
=2(x + 1)
2
11.
189
2 aaa ÷−
a
aa 18
9
)1( ×−=
= 2(a - 1)
2
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HUISWER
K
Vraestel 1 Boek P31 Oef 1 nr 1 - 10
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4
2)1
2
2
−−
x
xx
)2)(2(
)2(
+−−=xx
xx
)2)(2(
)2(
+−−−=xx
xx
)2( +−=x
x
xx
xx
x
xx 4
2712
12812)2
2
2
2
2
÷−
+×−−
)32(3
)1)(12(
−−+=
x
xx
4)94(3
)32(4)1)(12(22
x
x
xx
x
xx ×−+×−+=
4)32)(32(3
)32(4)1)(12(2
x
xx
xx
x
xx ×+−
+×−+=
1
1
)32(3
1
1
)1)(12( ×−
×−+=x
xx
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c
b
ay
c
c
ay
y
bca 863
4)3
2
3
32
×÷× x
x
−−
2
82)4
2
24ba=
c
b
c
ay
c
ay
y
bca 8
6
3
4
2
3
32
×××=
1
1
11
1
1
2 baaba ×××=
)2(2 +−= x
x
x
−−=
2
)4(2 2
2
)2)(2(2
−+−−=
x
xx
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bb
bb
bb
b
86
28296
72
494)5
2
2
2
2
−+−÷
+−
55
10)6
22 x
ax
x ÷
)72)(43(
)43(2
)72(
)72)(72(
−−−×
++−=
bb
bb
bb
bb
21
2
1
1
=
×=
ax
ax10
1
110
=
×=
2
2 5
5
10
xax
x ×=
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4
2
2
3
18
10
9
2)7
y
x
y
x ÷2
43
3
232 623)8
c
ba
c
ab
c
ba ÷×
5
2 2xy=
2
4
2
3
10
18
9
2
x
y
y
x ×=
5
2
1
1 2yx ×=
43
2
3
232
6
23
ba
c
c
ab
c
ba ××=
2
1
111
c
bc
b
c
=
××=
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2
2
25
14
5
7)9
a
x
a
x ÷42
3
42
6)10
22
++÷
−−+
x
xx
x
xx
x
a
a
x
14
25
5
7 22
×=
2
52
5
1
1
ax
ax
=
×=
xx
x
x
xx
3
42
42
62
2
++×
−−+=
)3(
)2(2
)2(2
)2)(3(
++×
−−+=
xx
x
x
xx
x
xx
x
2
)2(
1
1
+=
+×=
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Optel & Aftrek van breuke
Stap 1: As noemers nie dieselfde is nie,
kry KGV.
Stap 2: Verander elke breuk na ‘n
ekwivalente breuk waarvan die
noemer die KGV is.
Stap 3: Doen bewerkings met tellers.
Antwoord se noemer bly
dieselfde nl. KGV.
5
2
8
3 +
40=KGV
40
16
40
15 +=
40
1615 +=
40
31=
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Vir algebraiese breuke (+ en -)
KGV is 12
KGV = kleinste uitdrukking wat ‘n veelvoud
van elke uitdrukking is,
m.a.w. elke uitdrukking moet daarin voorkom
- Bepaal KGV van syfers
- Veranderlikes - elke noemer se veranderlikes moet
verteenwoordig wees.
Bv. KGV van:2 4x²y 3y²
x² y²
3a²b³
9a³b²
12ab²
KGV is 36 a³ b³
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Oef 5.30 (KGV Mondeling)
1. 5; 2; 3 KGV = 30
2. 2a; 3b; c KGV = 6abc
3. 4; 2; 3 KGV = 12
4. 2x²; 3y³ KGV = 6x²y³
5. x²; 5y²; 10xy KGV = 10x²y²
6. 3a²; 15ab²; 2b³ KGV = 30a²b³
7. p; 7p²q²; 2p²; 4q³ KGV = 28p²q³
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Vir algebraiese breuke (+ en -)
Kry selfde KGV
Met tellers: + en -
Onthou KGV
5432
2++−
aaba
ba
ba
1
5
ab
ab
a
4
a
a
ab
3
b
b
a
22
2
2⋅+⋅+⋅−⋅=
KGV is a²b
ba
ba
ba
ab
ba
a
ba
b2
2
222
5432 ++−=
ba
baabab2
25432 ++−=
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HUISWERK
OEF 5.32 Nr 9 – 15
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Oef 5.32
3
2aa +
3
2
3
3 aa +=
3
5a=
10. acbcab
432 ++ KGV abc
b
b
aca
a
bcc
c
ab•+•+•= 432
9.
abc
bac 432 ++=
11.
b
a
b
a
b
a
32
35 +− KGV 6b
b
a
b
a
b
a
6
2
6
9
6
30 +−=
b
aaa
6
2930 +−=
b
a
6
23=
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Oef 5.32
xx 2
3
3
21 ++
xxx
x
6
9
6
4
6
6 ++=
x
x
6
136 +=
12. KGV = 6x 13. 32
4321
xxx+−+
333
2
3
3 432
xx
x
x
x
x
x +−+=
KGV = x³
3
23 432
x
xxx +−+=
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Oef 5.32
15.
1a
4
a
32
−++
)1(
4
)1(
)1(3
)1(
)1(2
−+
−−+
−−=
aa
a
aa
a
aa
aa
)1a(a
a43a3a2a2 2
−+−+−=
)1a(a
3a5a2 2
−−+=
)1a(a
)3a)(1a2(
−+−=
14.
qp
23 + KGV = pq
pq
p
pq
q 23 +=
pq
pq 23 +=
KGV = a (a-1)
)1a(a
a4)1a(3)1a(a2
−+−+−=
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HUISWERK
Vraestel 1 Boek P32 Oef 2 nr 1, 2, 4, 8, 12 - 14
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Vraestel 1 Boek P 32 Oef 2
23
52)1
x
x
xx −+−−
6x KGV 23
52
1=−+−−= x
x
xx
6
3
6
10
6
]612[
6
6 22
x
x
x
x
x
x
x
x −+−−=
−
+
−−
=
x
xx
x
x
x
x
x
xx
3
3
22
2
3
5
6
62
6
6
1
x
xxxx
6
310]612[6 22 −+−−=
x
xxxx
6
3106126 22 −++−=
x
xx
6
16123 2 +−=
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Vraestel 1 Boek P 32 Oef 2
2
214)2
b
a
bb
a
b
a −×−
2
214
b
a
bb
a
b
a −
×−=
222
b KGV 24 =−−=b
a
b
a
b
a
24
22 b
a
b
a
b
b
b
a −−
=
2
222
24
24
b
aaabb
a
b
a
b
ab
−−=
−−=
2
34
b
aab −=
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Vraestel 1 Boek P 32 Oef 2
b
a
b
a
b
a
32
35)4 +−
6b KGV 32
35 =+−=b
a
b
a
b
a
2
2
33
3
2
3
6
65
+
−
=
b
a
b
a
b
a
6
2930
6
2
6
9
6
30
b
aaab
a
b
a
b
a
+−=
+−=
6
23
b
a=
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Vraestel 1 Boek P 32 Oef 2
4
2
3
13)8
xx −++
12 KGV 4
2
3
13 =−++= xx
3
3
4
2
4
4
3
13
−+
+= xx
12
)2(3
12
)13(4 xx −++=
12
36
12
412 xx −++=
12
10912
36412
+=
−++=
x
xx
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Vraestel 1 Boek P 32 Oef 2
ppp
3
3
4
4
5)12
2+−
22
12pKGV 3
3
4
4
5 =+−=ppp
12
123
4
4
3
4
3
3
4
52
+
−
=
p
p
pp
p
pp
12
361615
12
36
12
16
12
15
2
222
p
pp
p
p
p
p
p
+−=
+−=
12
20152p
p+=
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Vraestel 1 Boek P 32 Oef 2
2
1
1
1
3
1)13
2
−−
×−x
x
2
1
1
1
3
12
−
−
×−=x
x
2
1
1
1
3
)1)(1( −
−×+−=x
xx
6KGV 2
1
3
)1( =−+= x
3
3
2
1
2
2
3
)1(
−
+= x
6
3)1(26
3
6
)1(2
−+=
−+=
x
x
6
126
322
−=
−+=
x
x
![Page 41: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/41.jpg)
Vraestel 1 Boek P 32 Oef 2
63
4)4(
2
5
3
7)14
2
+−++−−b
bb
b
r!Faktorisee )2(3
)2)(2(
2
)4(5
3
7
++−++−−=
b
bbbb
6 KGV & Kanselleer 3
)2(
2
)4(5
3
7 =−++−−= bbb
−+
+−
−=
2
2
3
)2(
3
3
2
)4(5
2
2
3
7 bbb
6
)2(2
6
)4(15
6
)7(26
)2(2
6
)4)(5(3
6
)7(2
−++−−=
−++−−=
bbb
bbb
6
426015142 −+−−−= bbb
6
7811 −−= b
![Page 42: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/42.jpg)
HUISWERK
OEF 5.33 Nr 3, 5, 6, 13 - 16
![Page 43: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/43.jpg)
Oef 5.33
2
2
25
14
5
7
a
x
a
x ÷
x
a
a
x
14
25
5
7 22
×=
2
5ax=
3.
2
x 5 a
5.x
xx
3
36 2 +
x
xx
3
)12(3 +=
=2x + 1
6. x
y
y
x 44
3
2 −+
KGV: 3xy
xy
y
xy
x
xy
xy
3
12
3
12
3
2 22
−+=
xy3
y12x12xy2 22 −+=
![Page 44: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/44.jpg)
Oef 5.33
13.
yx
yx 3
2
4
3
2 −×
y
y 3
3
4 −=
yy
y
3
9
3
4 2
−=
y
yy
3
)32)(32( −+=
KGV: 3y
y
y
3
94 2 −=
14.a
b
b
a
b
a
52
5
2
12
2
×÷−
)52
5(
2
12
2
a
b
a
b
b
a ××−=
2
1
2
1 −=
= 0
![Page 45: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/45.jpg)
Oef 5.33
15.
1
7
22
7
2
3 2
2
2
2
x
x
y
y
x
y
x ÷×+y
22 7
1
4
7
2
3
xy
x
y
x ×+=
x
x
xyy
x
4
1
2
32
+=
22 4
)(1
4
)2(3
xy
y
xy
xx +=
2
2
4
6
xy
yx +=
![Page 46: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/46.jpg)
Oef 5.33
16.
b
a
c
aba
c
b
b
ac
b
a 2
5
2
5
3
3
2 222
+÷×−
c
ab
ac
b
b
ac
b
a 2)
52
5
3(
3
22
22
+××−=
c
ab
a
bc
b
a 26
3
2 +−=
abc
ba
abc
cb
abc
ca
3
6
3
18
3
2 22222
+−=
c
abc3
ba6cb18ca2 22222 +−=
![Page 47: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/47.jpg)
HUISWER
K
Vraestel 1 Boek P33 Oef 3 nr 1 - 4
![Page 48: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/48.jpg)
Vraestel 1 Boek P33 Oef
3
1)22 10144
248
3012
412
yxyx
yx
yx
xy
−+−−÷
−−
yx
yxyx
yx
xy
248
10144
3012
412 22
−−+−×
−−=
)3(8
)572(2
)52(6
)3(4 22
yx
yxyx
yx
xy
−+−−×
−−=
)3(8
))(52(2
)52(6
)3(4
xy
yxyx
yx
xy
−−−×
−−=
6
)( yx −=
![Page 49: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/49.jpg)
2)abba
baba
baba
baba
−÷
++−÷
++−−
2
244
2
422 22
22
22
baba
baba
baba
baba
2
2)2)(2(
))((
))(2(2
−÷
+−−÷
+++−=
2
2
)2)(2())((
))(2(2 ba
baba
ba
baba
baba −×−−
+×++
+−=
1=
Vraestel 1 Boek P33 Oef
3
![Page 50: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/50.jpg)
3)
−−×
−−−÷
++
)20(502
2
5
)1( 22
2
2
2
xxx
xx
xx
x
+−×
+−+−÷
+++= )4)(5(
)5)(5(2
)1)(2(
)5(
)1)(1(xx
xx
xx
xx
xx
+
++−÷+
++=)5(2
)4)(1)(2(
)5(
)1)(1(
x
xxx
xx
xx
++−
+×+
++=)4)(1)(2(
)5(2
)5(
)1)(1(
xxx
x
xx
xx
+−
+=)4)(2(
)1(2
xxx
x
Vraestel 1 Boek P33 Oef
3
![Page 51: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/51.jpg)
4)
132
42
5105
46
32
55222 ++
+÷++
−×−−
−bb
aba
bb
b
bb
ba
)21(2
)1)(12(
)1)(1(5
)23(2
)1)(32(
)(5
ba
bb
bb
b
bb
ba
+++×
++−×
+−−=
ab
b
bb
ba 1
)1(
)32(
)1)(32(
)( ×+
−−×+−
−=
2)1(
)(
+−−=
ba
ba
Vraestel 1 Boek P33 Oef
3
![Page 52: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/52.jpg)
HUISWER
K
Vraestel 1 Boek P33 Oef 3 nr 5 - 8
![Page 53: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/53.jpg)
5) 2
121
−−+ aa
2......2
12
1
1 =−−+= KGVaa
2
)12(
2
22 −−+= aa
2
1222 +−+= aa
2
3=
6)
16
8
44
42 −
−−
−+ x
x
x
x
x
)4)(4(
8
44
4
+−−
−+
+=
xx
x
x
x
x
)4)(4(
8)4()4(4
+−−++−=
xx
xxxx
)4)(4(
84164 2
+−−++−=
xx
xxxx
1)4)(4(
)4)(4(
)4)(4(
162
=+−+−=
+−−=
xx
xx
xx
x
![Page 54: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/54.jpg)
7) 23
2
1
1
1
)1(
1 xx
x
x
xx
x
x
+++−
−++
−
23
2
1
1
1
)1(
1 xx
x
x
xx
x
x
+++−
−+−
−=
22
2
1
1
)1)(1(
)1(
1 xx
x
xxx
xx
x
x
+++−
++−+−
−=
)1)(1(
)1)(1()1()1(2
22
++−−+−+−++=
xxx
xxxxxxx
)1)(1(
)1(2
2323
++−−−−−++=
xxx
xxxxxx
)1)(1(
12 ++−
=xxx
![Page 55: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/55.jpg)
8) 1
4
21
1
1
2
12
3222 +
−+−
+−
−+− xxxxxx
)1)(1)(1(
)1)(1(4)1()1(2)1(3
+−−−−−++−−+=
xxx
xxxxx
)1)(1)(1(
)12(412233 2
+−−+−−+++−+=
xxx
xxxxx
)1)(1)(1(
48412233 2
+−−−+−+++−+=
xxx
xxxxx
)1)(1)(1(
2104 2
+−−++−=xxx
xx
)1)(1)(1(
)152(2 2
+−−−−−=xxx
xx
![Page 56: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/56.jpg)
![Page 57: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/57.jpg)
![Page 58: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/58.jpg)
HUISWERK
EKSTRA OEF Nr 1 - 10
![Page 59: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/59.jpg)
x
xx
x
xxxx
x
xxxxx
x
xx
x
x
x
x
x
xx
x
x
xxa
6
12163
6
3106126
6
310)2(6)6(
6xKGV 6
)3(
6
)2(5
6
)2(6
6
)6(23
52)
2
22
2
−+=
−++−=
−+−−=
=−+−−=
−+−−
![Page 60: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/60.jpg)
2
2222
22
2
34
bKGV 24
24
214)
b
aabb
a
b
a
b
abb
a
b
a
b
ab
a
bb
a
b
ab
−=
=−−=
−−=
−×−
16
65a
16
8422
16aKGV 1616
)2(4
16
)1(2
164
2
8
1)
2
222
222
22
a
a
aaa
a
a
a
a
a
a
a
a
a
a
ac
+=
−++−=
=−++−=
−++−
![Page 61: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/61.jpg)
6
23
6bKGV 6
2
6
9
6
3032
35)
b
ab
a
b
a
b
ab
a
b
a
b
ad
=
=+−=
+−
52
25552
128131352
)32(4)1(1352
)32(4
52
)1(13
52KGV 13
32
4
113
32
4
1)
−=
−−−=
+−−=
+−−=
=+−−=
+−−
x
xx
xx
xx
xx
xxe
![Page 62: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/62.jpg)
6
10136
426156
)2(2)25(3
6KGV 6
)2(2
6
)25(3
3
2
2
25)
−=
−−−=
+−−=
=+−−=
+−−
x
xx
xx
xx
xxf
21
31221
2131271421
21)14(3)12(7
21KGV 21
21
21
)14(3
21
)12(7
17
14
3
12)
+=
++−+=
+−−+=
=+−−+=
+−−+
x
xx
xx
xx
xxg
![Page 63: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/63.jpg)
12
10912
36412
12KGV 12
)2(3
12
)13(44
2
3
13)
+=
−++=
=−++=
−++
x
xx
xx
xxh
x
xx
xx
xx
xxxx
xxxx
x
x
x
x
xx
x
x
xi
2
336
)33(36
996
31264
6
)14(364
6xKGV 66
)14(3
6
)32(26
1
2
14
3
32)
−−=
−−=
−−=
−−−−=
−+−−=
=−+−−=
−+−−
![Page 64: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/64.jpg)
2
3
2
3
22
22
2
6
6310
6
6
6
3
6
)2(5
6xKGV 2
1
3
52
1
3
5)
x
xx
x
x
xx
x
xxx
xxx
j
+−=
+−=
=+−=
+−
21
aKGV 21
21
)
2
2
a
aa
a
a
aa
a
aak
−+=
=−+=
−+
![Page 65: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/65.jpg)
12
2015
12
361615
12pKGV 12
)12(3
12
)4(4
12
)3(5
3
3
4
4
5)
2
2
2222
2
p
p
p
pp
p
p
p
p
p
pppl
+=
+−=
=+−=
+−
![Page 66: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/66.jpg)
6
12
6
322
6KGV 6
3
6
)1(22
1
3
12
1
1
1
3
)1(2
1
1
1
3
)1)(1(2
1
1
1
3
1)
2
−=−+=
=−+=
−+=
−×+=
−−
×+−=
−−
×−
xx
x
x
xx
xxx
xm
![Page 67: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/67.jpg)
6
78116
426015142
6KGV 6
)2(2
6
)4)(5(3
6
)7(23
)2(
2
)4(5
3
7
)2(3
)2)(2(
2
)4(5
3
763
4)4(
2
5
3
7)
2
−−=
−+−−−=
=−++−−=
−++−−=
++−++−−=
+−++−−
b
bbb
bbb
bbb
b
bbbbb
bb
bn
![Page 68: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/68.jpg)
![Page 69: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/69.jpg)
![Page 70: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/70.jpg)
HUISWER
K
OEF 5.28 Nr 1 – 6
![Page 71: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/71.jpg)
Oef 5.28
1.14
3
7
15
5
2 ÷×
23
14
7
15
5
2 ××=3 2
4=
2.27
4
3
8
4
1 ÷×
4
27
3
8
4
1 ××=92
2
9=b
3.2
2
3
2 6
6
2
3
3
b
x
b
a ÷÷
x 2
2
2
3bx
a=
62
6
3
2 2
23
2 b
xb
a ××=
y
4.53
2
10
14
5
3
2
7
y
xz
y
z
y
x ÷×
2
3xy=
xz
y
y
z
y
x
14
10
5
3
2
7 5
3
2
××=
2
5.2
2 6
5
2
5
4
x
x ÷÷
62
5
5
4 2
2
x
x××=
2
3
3
1=
14
)1(
7
6
3
)1( 22 −÷×− xx6.
2
2
)1(
14
7
6
3
)1(
−××−=x
x 2 2
4=x
![Page 72: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/72.jpg)
EKSTRA OEFENING
1. 2)2
(4)2
)(2
( yx
yx
yx −+−+
2. )42)(2(2))((3 22 bababababa +−+−−+
3. )()( 333 yxyx +−+
4. )()1(y
yx
y
x −÷−
5. yx
yx
yx
yx
yx
yx
33
632
++÷
−+÷
−+
![Page 73: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/73.jpg)
EKSTRA OEFENING
6. m
m
m
m
31
3
)31(5
545 2
+•
−−
7. a
a
a
aa
4
105
102
1032 +÷−
−−
8. p
p
p
pp
+−×
−−+
2
36
42
22
![Page 74: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/74.jpg)
EKSTRA OEFENING
1. 2)2
(4)2
)(2
( yx
yx
yx −+−+
)]2
(4)2
)[(2
( yx
yx
yx −++−=
]422
)[2
( yxyx
yx −++−=
]32
5)[
2( y
xy
x −−=
![Page 75: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/75.jpg)
EKSTRA OEFENING
. 2. )42)(2(2))((3 22 bababababa +−+−−+
)8(2)(3 3322 baba +−−=
3322 16233 baba −−−=
3. )()( 333 yxyx +−+
3322
332
)2)((
))((
yxyxyxyx
yxyxyx
−−+++=
−−++=
33322223 22 yxyxyyxxyyxx −−+++++=22 33 xyyx +=
)(3 yxxy +=
![Page 76: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/76.jpg)
EKSTRA OEFENING
. 4. )()1(y
yx
y
x −÷−
)()(yx
y
y
xy
−×−=
)()(yx
y
y
yx
−×−−=
1−=
5. yx
yx
yx
yx
yx
yx
33
632
++÷
−+÷
−+
yx
yx
yx
yx
yx
yx
++×
+−×
−+= 33
63
2
yx
yx
yx
yx
yx
yx
++×
+−×
−+= )(3
)2(3
2
1=
![Page 77: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/77.jpg)
EKSTRA OEFENING
. 6. m
m
m
m
31
3
)31(5
545 2
+•
−−
m
m
m
m
31
3
)31(5
)19(5 2
+•
−−=
m
m
m
mm
31
3
)13(5
)13)(13(5
+•
−−+−=
m
m
m
mm
31
3
)13(5
)13)(13(5
+•
−−+−=
m3−=
![Page 78: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/78.jpg)
EKSTRA OEFENING
. 7. a
a
a
aa
4
105
102
1032 +÷−
−−
)2(5
4
)5(2
)2)(5(
+×
−+−=
a
a
a
aa
)2(5
4
)5(2
)2)(5(
+×
−+−=
a
a
a
aa 2
5
2a=
p
p
p
pp
+−×
−−+
2
36
42
22
8.
p
p
p
pp
+−×
−−+=
2
)2(3
)2(2
)1)(2(
p
p
p
pp
+−−×
−−+=
2
)2(3
)2(2
)1)(2(
2
)1(3 −−= p
![Page 79: E algebraiese breuke](https://reader030.vdocuments.site/reader030/viewer/2022012312/55aa1e441a28abcc7e8b4878/html5/thumbnails/79.jpg)
x
MONDELIN
G
OEF 5.30 Nr 1 – 7