Master Rational Expressions: Online Quizzes and Practice

Question 1

Simplify the rational expression: (3x^2y) / (2xy^2)

Accepted Answer

3x/2y

Answer

3y/2x

Answer

3x^2/2y^2

Answer

3y^2/2x^2

Question 2

Determine the least common multiple (LCM) of the expressions x^2 - 9 and x^2 + 6x + 9.

Accepted Answer

(x - 3)^2(x + 3)

Answer

x^2 - 9

Answer

x^2 + 6x + 9

Answer

(x - 3)(x + 3)

Question 3

Simplify the complex fraction: (1 / (x - 2)) / (1 / (x + 2))

Accepted Answer

x + 2

Answer

x - 2

Answer

(x + 2)^2

Answer

(x - 2)^2

Question 4

Find an equivalent form of the rational expression (x + 1) / (x - 1).

Accepted Answer

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

Answer

(x - 1) / (x + 1)

Answer

-1 / (x - 1)

Answer

1 / (x + 1)

Question 5

Solve the following rational equation for x: (x + 1) / (x - 2) = 2

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 0

Answer

-3 < x < 3

Question 6

What is the domain of the following rational expression: (x^2 + 2x) / (x(x - 3))

Accepted Answer

{x | x ≠ 0, x ≠ 3}

Answer

x = 0, x = 3

Answer

{x | x > 0, x < 3}

Answer

{x | x < 0, x > 3}

Question 7

Which of the following operations can be used to simplify the rational expression: ((x + 2) / (x - 1)) * ((x - 1) / (x + 3))

Accepted Answer

Cancel the common factors in the numerators and denominators.

Answer

Add the numerators and multiply the denominators.

Answer

Subtract the numerators and multiply the denominators.

Answer

Multiply the numerators and denominators.

Question 8

Multiply the rational expressions: (a - b) / (a + b) * (a + b) / (a - b)

Accepted Answer

1

Answer

-1

Answer

(a - b)² / (a + b)²

Answer

(a + b)² / (a - b)²

Question 9

Simplify the complex fraction: (1 / (x + 1)) / (1 / (x - 1))

Accepted Answer

(x + 1) / (x - 1)

Answer

(x - 1) / (x + 1)

Answer

1 / (x + 1)

Answer

1 / (x - 1)

Question 10

Determine the domain of the rational function: y = (2x - 1) / (x² - 4)

Accepted Answer

All real numbers except x = 2 and x = -2

Answer

All real numbers except x = 1 and x = -1

Answer

All real numbers

Answer

No real numbers

Question 11

Which expression is NOT equivalent to the rational expression (3x² - 2x + 1) / (x² - 1)?

Accepted Answer

3 + 2 / (x - 1)

Answer

3 + (2x - 1) / (x² - 1)

Answer

3x - 2 + 1 / (x² - 1)

Answer

3x + 2 + 1 / (x + 1)

Question 12

Solve the rational equation for x: (x - 1) / (x + 2) = 2

Accepted Answer

x = 3

Answer

x = -3

Answer

x = -1

Answer

x = 1

Question 13

Divide the rational expressions: (x^2 - 4) / (x + 2) ÷ (x + 2) / (x - 2)

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 - 2

Answer

x^2 + 2

Question 14

Which of the following is NOT a rational expression?

Accepted Answer

2^x

Answer

2/3

Answer

x/(x-1)

Answer

(x+1)/(x-1)

Question 15

Simplify the expression: (2/3) ÷ (4/9)

Accepted Answer

3/2

Answer

6/3

Answer

2/6

Answer

9/3

Question 16

Solve for x: (x-1)/(x+2) = 2/3

Accepted Answer

x = 5

Answer

x = -5

Answer

x = 7

Answer

x = -7

Question 17

Which of the following expressions is equivalent to (x^2 - 1)/(x - 1)?

Accepted Answer

x

Answer

x + 1

Answer

x - 1

Answer

(x - 1)(x + 1)

Question 18

Find the domain of the expression: (x+3)/(x^2 - 9)

Accepted Answer

x ≠ ±3

Answer

x ≠ 0

Answer

x ≠ 1

Answer

All real numbers

Question 19

Multiply the rational expressions: (x - 2) / (x + 3) * (x + 3) / (x - 5) = ?

Accepted Answer

x - 2 / x - 5

Answer

x + 3 / x - 2

Answer

x - 2 / x + 3

Answer

x + 3 / x - 5

Question 20

Subtract the rational expressions: (6a / b) - (2a / 3b)

Accepted Answer

4a / 3b

Answer

4a / b

Answer

2a / b

Answer

2a / 3b

Question 21

Simplify the rational equation: (x + 1) / (x - 1) = 2

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 1

Answer

No solution

Question 22

Evaluate the following rational expression for x = 3: (x^2 - 4) / (x - 2)

Accepted Answer

5

Answer

-5

Answer

1

Answer

-1

Question 23

Which of the following is equivalent to the rational expression: (x^2 - 1) / (x + 1)?

Accepted Answer

x - 1

Answer

x + 1

Answer

x^2 - 1

Answer

x^2 + 1

Question 24

Add the following rational expressions: (2 / x) + (3 / (x + 1))

Accepted Answer

5x / x(x + 1)

Answer

5 / x(x + 1)

Answer

8x / x(x + 1)

Answer

8 / x(x + 1)

Question 25

Solve the rational equation: (x + 1)/(x - 2) = 3.

Accepted Answer

x = 5

Answer

x = 3

Answer

x = -5

Question 26

Identify the expression that is not a rational expression.

Accepted Answer

x^2 + 2x - 3

Answer

2/(x^2 - 1)

Answer

x/(x - 1)

Answer

x^2 - 1/x + 2

Question 27

Factor the denominator of the rational expression: (x^2 + 2x)/(x^2 - 4).

Accepted Answer

(x + 2)(x - 2)

Answer

x(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x + 2)^2

Question 28

Find the product of (x + 2)/(x - 1) and (x - 1)/(x + 2)

Accepted Answer

1

Answer

x²

Answer

x

Answer

x - 1

Question 29

Solve for x in the equation: (x + 3)/(x - 2) = 2

Accepted Answer

x = 7

Answer

x = 2

Answer

x = -7

Answer

x = 5

Question 30

Which of the following represents the rational expression for the area of a triangle with a base of (x - 2) units and a height of (x + 3) units?

Accepted Answer

(x - 2)(x + 3)/2

Answer

(x + 2)(x + 3)/2

Answer

(x + 2)(x - 3)/2

Answer

(x - 2)(x - 3)/2