warm up factor the expression. answer 5x (2 – x) answer (x + 6)(x – 8) 1. 10x – 5x 2 2. x 2...
TRANSCRIPT
Warm up Factor the expression.
ANSWER 5x (2 – x)
ANSWER (x + 6)(x – 8)
1. 10x – 5x2
2. x2 – 2x – 48
Lesson 8.4, For use with pages 573-580
3. x3 – 125
ANSWER (x – 5)(x2 + 5x + 25)
Factor the expression.
4. What is the volume and surface area of a cardboard shipping carton that measures 15 inches by 18 inches by 20 inches?
ANSWER 5400 in.3, 1860 in.2
8.5 – Adding and Subtracting Rational Expressions
EXAMPLE 1 Add or subtract with like denominators
Perform the indicated operation.
74x
+3
4xa. 2x
x + 6– 5
x + 6b.
SOLUTION
74x
+3
4xa. =
7 + 34x
104x=
52x= Add numerators and
simplify result.
x + 6 2x – 5=2x
x + 65
x + 6–b. Subtract numerators.
GUIDED PRACTICE for Example 1
Perform the indicated operation and simplify.
16x
a. 712x
+5
12x=
7 – 512x
= 212x
= Subtract numerators and simplify results .
1 x2
b. 2 3x2
+1
3x2=
2 + 13x2 =
33x2
= Add numerators and simplify results.
c. 4x x–2
–x
x–2=
4x–xx–2
= 3xx–2
= Subtract numerators. 3x
3x – 2
EXAMPLE 2 Find a least common multiple (LCM)
Find the least common multiple of 4x2 –16 and 6x2 –24x + 24.
Factor each polynomial. Write numerical factors asproducts of primes.
EXAMPLE 3 Add with unlike denominators
Add: 9x2
7+
x3x2 + 3x
SOLUTION
EXAMPLE 4 Subtract with unlike denominators
Subtract: x + 22x – 2
–2x –1x2 – 4x + 3
–
SOLUTION
GUIDED PRACTICE for Examples 2, 3 and 4
Find the least common multiple of the polynomials.
5. 5x3 and 10x2–15x
GUIDED PRACTICE for Examples 2, 3 and 4
Find the least common multiple of the polynomials.
6. 8x – 16 and 12x2 + 12x – 72
GUIDED PRACTICE for Examples 2, 3 and 4
4x3
–717.
SOLUTION
GUIDED PRACTICE for Examples 2, 3 and 4
13x2
+x
9x2 – 12x8.
GUIDED PRACTICE for Examples 2, 3 and 4
xx2 – x – 12
+ 512x – 48
9.
SOLUTION
GUIDED PRACTICE for Examples 2, 3 and 4
12x + 5x + 1512(x + 3)(x – 4)
=
17x + 1512(x +3)(x + 4)
=
Add numerators
Simplify
GUIDED PRACTICE for Examples 2, 3 and 4
x + 1x2 + 4x + 4
– 6x2 – 4
10.
SOLUTION
EXAMPLE 5 Simplify a complex fraction (Method 1)
Let f be the focal length of a thin camera lens, p be the distance between an object being photographed and the lens, and q be the distance between the lens and the film. For the photograph to be in focus, the variables should satisfy the lens equation below. Simplify the complex fraction.
Physics
Lens equation: f1
1p
1q+
=
GUIDED PRACTICE for Examples 5 and 6
x6
x3
–
x5
710
–
– 5x 3 (2x – 7)
=
Multiply numberator and denominator by the LCD
Simplify
x6
x3
–
x5
710
–
11.
x6
x3
–
x5
710
–
3030=
GUIDED PRACTICE for Examples 5 and 6
2x
–
2x
+
4
3
12.
GUIDED PRACTICE for Examples 5 and 6
3x + 5
2x – 3
+ 1x + 5
13.