MCR3U1
Name:_______________________________
Date:________________________________
Unit 2 – Rational Expressions REVIEW
PART 1: KNOWLEDGE AND UNDERSTANDING
1. The correct product of
(a  3)(a  2) (a  5)(a  1)
simplifies fully to the form:

(a  1)(a  1) (a  2)(a  2)
(a  3)(a  5)
(a  1)(a  2)
(a  3)(a  5)
c)
(a  1)(a  2)
(a  3)(a  5)
(a  1)(a  2)
(a  3)(a  5)
d)
(a  1)(a  2)
a)
b)
2. Which expression has restrictions m  2, m  2 ?
3m
4(m  2)

m2
6m
(3m  1)
2m  1
c)

(2m  1) 3m(m  1)
10m
5

m  2 2(m  2)
5m(m  3) (m  5)
d)
 2
4m
(m  2)
a)
b)
3. Which rational expression has no restrictions?
a)
x 2  6x  9
4x
b)
4. Given the rational expression
4
( x  3) 2
c)
9x 2
 9x 2
d)
x5
the restrictions on the variable are:
3x 2  6 x
a) x  3 and x  0
c) x  2 and x  0
b) x  2 and x  2
d) x  0
5. The lowest common denominator required to perform the operation
3x
4x  1
is:
 2
x  3 x  5x  6
a) ( x  2) 2 ( x  3)
b) ( x  2)( x  3)
c)
d) ( x 2  5x  6)( x  2)
( x  2)( x  3)
6. The rational expression
a)
1
x 1
x2
1 x2
x 1
can be reduced to the form:
x2 1
b) x  1
c)
(1  x)
( x  1)( x  1)
d)
1
x 1
1
MCR3U1
Name:_______________________________
7. The quotient
1  3x
2
has a total of:

2
x  9 4  x2
a) Two restrictions
c) Four restrictions
b) Three 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)
x2 1
2
a) 2 x  3x  1
x 2  9 x  14 x(7  x)

2
4( x  4)
x

7
x

12
c)
b)
2
x
 2
( x  3) x  8 x  15
d)
 x 2  x  12 (2 x  1)( x  3) 
x2
 2


x  2  x  2x
4x 3  2x 2 
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.
3 y
 1,
y

3
a)
y0
( y  4) 2
 1,
2
y

16
b)
y4
2
MCR3U1
Name:_______________________________
10. The length of a flag can be represented by the expression 9  3x and the area can be
2
represented by the expression 3x  30 x  63 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 x  0 and
x
1
2.
1 
 1
12. Solve for x if the reciprocal of  x  is -2.
3
MCR3U1
Name:_______________________________
13. Simplify fully and state the restrictions. Show your factored steps, but not your factoring work.
a)
c)
24xy 2z 3
b)
16x yz
3
2a + ab - 3b
2
b -a
2
2
2
d)
20mn
24n
1+
1-
2
´
3n
5m 2
1
x
1
x2
14. Simplify fully and state all restrictions.
w 2 + 4w - 21
9w 2 - 1
¸
w 2 + 2w - 35 3w 2 - 16w + 5
4
MCR3U1
Name:_______________________________
15. Simplify and reduce fully, and state all restrictions.
y +4
-
6
y + y - 2 y - 5y - 14
2
2
PART 2: APPLICATION
16. A rectangular prism has length =
2x - 5
, width =
3x + 2
, and height =
x +4
, all in metres.
3x + 1
x +4
3x - 1
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.
5
MCR3U1
Name:_______________________________
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.
6
MCR3U1
Name:_______________________________
PART 3: THINKING
14. Given triangle ABC below, determine a simplified expression that represents the perimeter
of ABC . State restrictions, if any.
A
g 1
g 3
g
g 1
C
B
g 1
2g  6
7
MCR3U1
Name:_______________________________
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?
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