MCR3U1 Name:_______________________________

Date:________________________________

1

Unit 2 – Rational Expressions REVIEW

PART 1: KNOWLEDGE AND UNDERSTANDING

1. The correct product of )2)(2(

)1)(5(

)1)(1(

)2)(3(

aa

aa

aa

aasimplifies fully to the form:

a) )2)(1(

)5)(3(

aa

aa b)

)2)(1(

)5)(3(

aa

aa

c) )2)(1(

)5)(3(

aa

aa d)

)2)(1(

)5)(3(

aa

aa

2. Which expression has restrictions 2,2 mm ?

a) m

m

m

m

6

)2(4

2

3

b)

)2(2

5

2

10

mm

m

c) )1(3

12

)12(

)13(

mm

m

m

m d)

)2(

)5(

4

)3(52

m

m

m

mm

3. Which rational expression has no restrictions?

a) x

xx

4

962 b)

2)3(

4

x c)

2

2

9

9

x

x

d)

2

2

1 x

x

4. Given the rational expression xx

x

63

52

the restrictions on the variable are:

a) 3x and 0x b) 2x and 2x

c) 2x and 0x d) 0x

5. The lowest common denominator required to perform the operation 65

14

3

32

xx

x

x

xis:

a) )3()2( 2 xx b) )3)(2( xx

c) )3)(2( xx d) )2)(65( 2 xxx

6. The rational expression 1

12

x

xcan be reduced to the form:

a) 1

1

x b) 1x c)

)1)(1(

)1(

xx

x d)

1

1

x

MCR3U1 Name:_______________________________

2

7. The quotient 22 4

2

9

31

xx

x

has a total of:

a) Two restrictions b) Three restrictions c) Four restrictions d) Five restrictions

8. Simplify fully and state restrictions. You must show how you:

Factored fully including: common factors, simple trinomials, decomposition,

difference of squares

Reduced each rational expression to lowest terms (where applicable)

Simplified fully (either by reducing, multiplying/dividing, or adding/subtracting)

a) 132

12

2

xx

x

b) 158)3(

22

xx

x

x

c) )4(4

)7(

127

1492

2

x

xx

xx

xx

d)

232

22

24

)3)(12(

2

12

2 xx

xx

xx

xx

x

x

9. In each of the examples below errors were made. Either the final answer is wrong, or the

restriction is wrong, or both. Correct all errors for each rational expression.

a) ,1

3

3

y

y

0y b) ,1

16

)4(2

2

y

y

4y

MCR3U1 Name:_______________________________

3

10. The length of a flag can be represented by the expression x39 and the area can be

represented by the expression 63303 2 xx respectively.

a) Write a simplified expression to represent the width of the flag. State

restrictions.

b) Find a simplified expression to represent the perimeter of the flag.

c) Do any restrictions on the variable apply? Justify.

11. Write a single rational expression with the two restrictions 0x and 2

1x

.

12. Solve for x if the reciprocal of

1

1

x is -2.

MCR3U1 Name:_______________________________

4

13. Simplify fully and state the restrictions. Show your factored steps, but not your factoring work.

a)

24xy 2z 3

16x 3yz b)

20mn

24n2´

3n

5m2

c)

2a2 + ab - 3b2

b2 - a2 d)

1 +1

x

1 -1

x 2

14. Simplify fully and state all restrictions.

w 2 + 4w - 21

w 2 + 2w - 35¸

9w 2 - 1

3w 2 - 16w + 5

MCR3U1 Name:_______________________________

5

15. Simplify and reduce fully, and state all restrictions.

y + 4

y 2 + y - 2-

6

y 2 - 5y - 14

PART 2: APPLICATION

16. A rectangular prism has length =

2x - 5

x + 4, width =

3x + 2

3x - 1, and height =

x + 4

3x + 1, all in metres.

a) Determine a simplified expression for the volume of the rectangular prism. Express your

answer as a quotient of two polynomials in standard (not factored) form, and state any

restrictions.

b) Determine the volume when x = 4 metres.

MCR3U1 Name:_______________________________

6

17. There are 2 rational expressions, P/Q and R/S, where Q = x2 – 16, R = x + 2, and

S = x2 – x – 12. If P/Q + R/S = A/B, where A = 6x2 + 19x + 2, determine an expression for P.

18. The area of a rectangular field is given by the expression x2 + 8x + 15.

a) Determine the expressions that represent the dimensions of the field.

b) Determine a fully simplified expression for the perimeter of the field.

MCR3U1 Name:_______________________________

7

PART 3: THINKING

14. Given triangle ABC below, determine a simplified expression that represents the perimeter

of ABC . State restrictions, if any.

62

1

g

g

B

1g

g

C

A

3

1

g

g

MCR3U1 Name:_______________________________

8

15. Hanz and Franz are walking 60 km to raise money to fight Breast Cancer. Franz walks 1 km/h

faster than Hanz, but stops for 30 min to sign autographs. They start at the same time, but Franz

finishes 2 ½ hours before Hanz. How fast was each person walking, and how long did it take for each

person to finish the walk?