Math 30-2
Math 30-2
Unit 1: Rational Expressions
REVIEW
Multiple Choice
2 x
3x
1. Identify the rational expression that is equivalent to
A.
4  2x
3x
C.
2  2x
6x
B.
4  2x
6x
D. 6x  3x 2
4x
.
x5
2x
C.
0.5x  2.5
2. Identify the rational expression that is equivalent to
A.
B.
x
x5
4x 2
D.
x  5x 2
3. Identify the rational expression that is equivalent to
A.
B.
9  3x
12x 2  x
3 x
C.
6x 2  2x
3x  x 2
4x 3  0.3x 2
4. Determine the non-permissible value(s) for
4 x(x  5)
x5
D.
.
9x  3x 2
12x 3  x
6(3  x)
2x(12x  1)
2 x
3x
A. x  2
C. x  0
B. x  0, x  2
D. x  0
Math 30-2
2x  8x 2
5. Determine the non-permissible value(s) for
4x  2
A. x  0
B. x 
1
2
C. x  
1
2
D. x  
1
2
6. Which rational expression is simplified?
i)
2x
6x  4x 3
ii)
5  15x 2
iii)
10x
10x
7x 2 1
A. i) and ii)
B. ii)
C. i) and iii)
D. i)
7. Simplify
A.
B.
3
2k 2
3k
2k 2
B.
14k 3
.
, k0
C.
, k0
D.
8. Simplify
A.
21k
16h2  40h
h5
3h 2
24h 3
, h0
2h  5
3h 2
, h0
7
k2
, k0
21
14k 2
, k0
.
C.
D.
2h 10
6h 2
, h0
2h  5
, h0
3h
Math 30-2
6a  54a 2
9. Simplify
.
18  24a
1 9a
3
, a
3  4a
4
C.
3a 18a 2
3
, a
6  8a
4
2a  27a 2
3
B.
, a
9  12a
4
D.
a  9a 2
3
, a
3  4a
4
A.
10. Simplify
3n  1
2n

.
n  5 6n  2
A.
n
1
, n  5,
(n  5)(3n 1)
3
C.
2n
1
, n  5,
n5
3
B.
2n
1
, n  5,
3n  1
3
D.
n
1
, n  5,
n5
3
11. Simplify
6d  3 2d  1

.
3d
4
A.
1
1
, d  0,
2d
2
C.
3
1
, d  0,
d 1
2
B.
4
1
, d  0,
3d
2
D.
4
1
, d  0,
d
2
12. Determine the lowest common denominator for the pair
A. 9a 3  6a2
C. 6a 3
B. 3a 3  2a2
D. 3a2
a
80
and
.
3a  2
3a 2
Math 30-2
2m
13. Simplify
12m 2

m
2
1 3m 2
A.
, m0
6m
B.
m
A.
B.
, m0
12m 2
14. Simplify
1
p2  4
p
p2  4
D.
p2  4
4m2
, m0
24m2
p
, p  2
p2  p  4
15. Simplify
1 6m 2
C.
, m0
12m
C.
, p  2
D.
1 p
p2  4
, p  2
1 p 3  4 p
p2  4
, p  2
y
y5
.

y  5 y2  25
A.
y 1
, y  5
y5
C.
B.
y 1
, y  5
y5
D.
y 1
y2  5
y 1
y2  5
16. Solve the following equation for x.
2
1
7


x x  1 2x  2
A. x  2
C. x  4
B. x  3
D. x  5
17. Solve the following equation for x:
3x
2
x 1
A. x  2
C. x  4
B. x  3
D. x  5
, y  5
, y  5
Math 30-2
Written Response
1. Simplify the following rational expressions. State the non-permissible values.
a.
21c2 (c  5) 9(2c 1)

7c(1 2c)
3c
b.
Non-permissible Values:
c.
4d
3

2d  8 2d 2
Non-permissible Values:
6(5  3d) 12d(3d  5)

2d  6
d3
Non-permissible Values:
d.
2a
1

3  a 5(a  2)
Non-permissible Values:
2. In question 1 of the written response you added, subtracted, multiplied and divided
rational expressions. How is this similar to performing the same operations of rational
numbers?
Math 30-2
3. Use the following rational equation to answer the next two questions.
6
x 2 1

1
1

x 1 2
a. Why are 1 and -1 non-permissible values of the equation?
b. Solve the equation.
4. Write a rational expression with a variable of b and with restriction x 
2
.
3
5. Brian tried to determine the non-permissible values for an expression, as shown below.
Identify Brian’s error, and correct his solution.
Math 30-2
6. When they work together, Samir and Lorraine can deliver flyers to all the homes in their
neighbourhood in 24 min. When Lorraine works alone, she needs 14 min longer to deliver
the flyers than Samir when he works alone.
Let y represent the time that Samir takes to deliver the flyers on his own. Write a rational
equation to solve for y.
2
7. Two rectangles have the same width. The smaller rectangle has an area of 20cm and a
2
length l centimeters. The larger rectangle has an area of 30cm and a length (l  5)
centimeters.
a. Explain why the equation
b. Solve the equation
30
20
can be used to represent the information.

l 5 l
30
20
to find the length of each rectangle.

l 5 l
c. What is the width of each rectangle?