PRACTICE PROBLEMS ON RATIONAL EXPRESSIONS FOR SAT

Problem 1 :

Which of the following is equivalent to

(1/x) / (x + 3)

(a) 1/x(x + 3)  (b)  x/(x + 3)  (c) (x  +3)/3  (d) x(x +3)

Solution

Problem 2 :

The equation

(kx² + 14x - 20)/(3x - 2) = (5x + 8) - [4/(3x - 2)]

is true for all values of x ≠ 2/3, where k is a constant, what is the value of k ?

(a) 8  (b)  9  (c) 11  (d) 15

Solution

Problem 3 :

The expression (3x² + 4)/(x + 1) is equivalent which of the following ?

(a)  (3x - 3) + 1/(x + 1)    (b) 3x - 3 + 7/(x + 1)

(c)  (3x + 3) + 1/(x + 1)    (b) 3x + 3 + 7/(x + 1)

Solution

Problem 4 :

When 3x² + x + 2 is divided by x - 1, the result can be expressed as

(ax + b) + [c/(x - 1)]

where a, b and c are constants. What is the value of

a + b + c ?

Solution

Problem 5 :

When 2x² - 5x + 3 is divided by 2x + 1, the result can be written as

(x - 3) + [R/(2x+ 1)]

where R is a constant. What is the value of R ?

Solution

Problem 6 :

What is the one of the possible solution to the equation.

22/(x + 3) - 6/(x - 2) = 1

Solution

Problem 7 :

The expression

(x + 1)/(x + 2) - (x - 2)/(x - 1)

is equivalent to which of the following ?

(a)  -5/(x + 2) (x - 1)    (b)  1/(x + 2) (x - 1)

(c)  3/(x + 2) (x - 1)    (b)  (2x²+3)/(x + 2) (x - 1)

Solution

Problem 8 :

When 5x + 3 is divided by x + m, where m is a constant, the result can be written as

5 + [ r/(x + m) ]

where r in terms of m ?

Solution

Problem 9 :

(x² - x - a) / (x - 2) = (x + 1) - [8/(x - 2)]

In the equation above, what is the value of a ?

Solution

Problem 10 :

The equation

(24x² + 25x - 47) / (ax - 2) = (-8x - 3) - 53/(ax - 2)

is true for  all values of x ≠ 2/a, where a is constant. What is the value of a ?

Solution

Answers