A set of questions, with answers, on reducing rational expressions similar to the questions in the compass math test are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

For all x not equal to 1, which of the following is equivalent to the rational expression below?
x^{2} + 5x  6

 
x  1 
A) x  6
B) x  1
C) x + 6
D)  x  6
E) 6  x

Which of the following is a simplified expression equal to
for all x not equal to 5?
A) 1/2
B) 1 / (x  5)
C) 2
D)  1 / (x  5)
E) 1/2

For all x not equal to  4, which of the given expressions is equivalent to the expression below?
16  x^{2}

 
x + 4 
A) x  4
B) 16  1
C) x + x
D)  x  4
E) 4  x

Simplify the following rational expression.
x + 2 
 = 
x^{2} + 2x

A) 1 / 2x
B) 1 / 2x for all x not equal to  2
C) 1 / x
D) 1 / x , for all x not equal to  2
E) 1 / 2

For all x not equal to 3, which of the given expressions is equivalent to the expression below?
3  x 
 
x^{2} x  6

A)  1 / (x + 2)
B) 1 / (x  2)
C) 1 / (x  2)
D) 1 / (x  3)
E) 1 / (x  3)

x^{3}  x

 = 
x^{2}  1

A) x
B) x , for all x not equal to 1
C) x , for all x not equal to 1 or 1
D) 1 / x
E) x  1

x^{2}  4

 = 
x^{2} + 4x  12

A) (x + 2) / (x + 6) , for all x
B) (x + 2) / (x + 6) , for all x not equal to 2
C) (x + 2) / (x + 6) , for all x not equal to  2
D) (x + 2) / (x + 6) , for all x not equal to 0
E) 1 / 3

Simplify the following rational expression.
x^{2} + 1

 
x^{3} + x

A) 1 / x for all x not equal to 1
B) x + 1 , for all x not equal to  1
C) 1 / 2x
D) 1 / (x + 1) for all x not equal to 1
E) 1 / x

x^{2} + 2x  3

 = 
2x^{2} + 3x  5

A) (x + 3) / (2x + 5) , for all x not equal to 1
B) (x + 3) / (2x + 5) , for all x
C) x + 3 , for all x not equal to 1
D) 1 /(2x + 5) , for all x
E) (x + 3) / (2x + 5) , for all x not equal to 3

For all x not equal to 1, which of the following is equivalent to the rational expression below?
x  1 
 
(x^{2}  1)(x + 3)

A) 1 / (x + 3)
B) 1 / (x^{2} + 4 x + 3)
C) 1 / (x + 1)
D) 1 / x
E) 1 / (x  1)

