Math 060 Review
Chapter 9
1. Reduce each rational expression to lowest terms. Assume that the variables are restricted to
values that prevent division by 0.
21x9 y 3
a)
28 x13 y
6x2
b)
6 x 4  18 x3
4a 2  4ab  b 2
c)
2a 2  ab  b 2
x5
d)
25  x 2
x4 1
e) 3
x x
37y
f)
14 y 2  6 y
2. Simplify each expression as completely as possible. Assume that the variables are restricted to
values that prevent division by 0.
6 xy 4 x 2  y 2
a)

2x  7
3x 2
9 x2  4
3x  2
b)

16 xy 16 x 2 y  8 xy
x  y 1
c)
x  y 1
1
1

d) a a  1
1 1

a a2
1
x
x2  2
e)

 2
x 1 x  2 x  x  2
1
3
2y
f)

 2
x  y x  y y  x2
g)
h)
i)
j)
k)
3w  5 z
9w2  25 z 2

6w2 z 18w2 z  30wz 2
3x  8
4x  2
 2
2
x  6 x  8 x  x  12
3
12 
x 1
x
x

x2 x2
1
 49
x2
1
7
x
3. Solve each equation.
2
y
a)

5
y2 y2
5
3
b)
 1
4x 1
8x  2
x  1 14
3x  7

 2
c)
x
x  7 x  7x
4
3
8
d)


2
x  7 x  10 x  2
x5
x2 x3
e)

1
x 1 2x  5
x  11
5
3
f)


2
x  5x  4 x  4 1  x
4. Solve each equation for the specified variable.
1 1 1
a)
Solve for z:
 
x y z
E
b)
Solve for x: A 
x y
a
a 1

c)
Solve for b:
b 1
b
5. The sum of the reciprocals if two consecutive even integers is
7
. Find those integers.
24
6. The denominator of a fraction is 6 more than the numerator, and the fraction equals -1. Find the
numerator.
7. The sum of the reciprocals of two consecutive odd inters is 12 times the reciprocal of their product.
Find those integers.
8. A rope 20 m long is cut into two pieces whose lengths have a ratio of 4 to 1. Find the length of each
piece.