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

Problem 1 :

If y > 5, which of the following is equivalent to 

1 / [(1/(y - 4) + 1/(y - 3)]

a)  2y - 7    b) y² - 7y + 12       c)  y² - 7y + 12/(2y - 7)      d)  (2y - 7) / y² - 7y + 12

Solution

Problem 2 :

For what vaue of x is the expression

2 / [(x - 6)² + 4(x - 7) + 8]

undefined ?

Solution

Problem 3 :

If 7/y = 17/(y + 30), what is the value of y/7 ?

a)  1/3       b)  3       c) 7        d)  21

Solution

Problem 4 :

(80x² + 84x - 13)/(kx - 4) = -16x - 4 - [29/(kx - 4)]

Teh equation above is true for all values of x ≠ 4/k, where k is constant. What is the value of k ?

a)  -5       b)  -2       c) 2        d)  5

Solution

Problem 5 :

If (x + y)/x is equal to 6/5, which of the following is true ?

a)  y/x = 1/5          b)  y/x = 11/5       c)  (x + y) / x = 1/5       d)  (x - 2y)/x = -1/5

Solution

Problem 6 :

Which of the following must be true if (t + u)/t = 12/11 ?

a)  u/t = 1/11          b)  u/t = 23/11      c)  (t - u) / t = 1/11       d)  (t + 2u)/t = -8/11

Solution

Problem 7 :

The equation

(36y² + 43y - 25)/(ky - 3) = (-9y - 4) - [37/(ky - 3)]

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

a)  27          b)  4     c)  -4       d)  -27

Solution

Problem 8 :

(4c + 1)/(2c - 3)² - 2/(2c - 3)

The expression above is equivalent to x/(2x - 3)², where x is a positive constant and c ≠ 3/2, what is the value of x ?

Solution