Master Rational Expressions: Practice Quiz for High School Freshmen

Question 1

Which is the least common denominator of the expressions (x-1)/(x^2-x-2) and (x+2)/(x^2-5x+6)?

Accepted Answer

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

Answer

(x-1)(x-2)

Answer

(x-1)(x+2)

Answer

(x-1)(x-2)(x-3)

Question 2

Which of the following is a rational expression?

Accepted Answer

x/(x+1)

Answer

x^2 + 1

Answer

sqrt(x)

Answer

1/0

Question 3

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

Accepted Answer

All real numbers except x = 3, -3

Answer

All real numbers except x = 0

Answer

All real numbers

Answer

All real numbers except x = 3

Question 4

Which of the following is an example of a complex fraction?

Accepted Answer

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

Answer

x + 2/x - 3

Question 5

Multiply: (2x + 4)/(x - 1) * (3x - 3)/(x + 2)

Accepted Answer

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

Answer

6

Question 6

Simplify the expression: (x^2 - 4)/(x + 2) ÷ (x - 2)/(x^2 + 4)

Accepted Answer

x + 2

Question 7

Simplify the rational expression: (x^2 - 9) / (x - 3)

Accepted Answer

x - 3

Answer

x + 3

Answer

x - 9

Answer

x + 9

Question 8

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

Accepted Answer

x - 1

Answer

x + 1

Answer

x - 2

Answer

x + 2

Question 9

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

Accepted Answer

(x + 1) / 2

Answer

(x - 1) / 2

Answer

2(x + 1)

Answer

2(x - 1)

Question 10

Which of the following is a rational function?

Accepted Answer

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

Answer

f(x) = x^2 + 2x + 1

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Question 11

Simplify the rational expression (x^2 - 9) / (x + 3).

Accepted Answer

x - 3

Answer

x + 3

Answer

x - 9

Answer

x + 9

Question 12

Which of the following rational expressions is undefined?

Accepted Answer

(3x^2) / (x^2 - 9)

Answer

(x - 5) / (x + 2)

Answer

(x^2 - 4) / (x - 2)

Answer

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

Question 13

If the sum of two rational expressions is (3x + 2) / (x - 1), and one of the expressions is (x + 1) / (x - 1), what is the other expression?

Accepted Answer

2x / (x - 1)

Answer

x / (x - 1)

Answer

2x + 1 / (x - 1)

Answer

x + 2 / (x - 1)

Question 14

Simplify the rational expression: (x^2 - 9) / (x + 3)

Accepted Answer

x - 3

Answer

x + 3

Answer

(x - 3)(x + 3)

Answer

Cannot be simplified

Question 15

For which value of x is the rational expression (x - 3) / (x + 2) undefined?

Accepted Answer

-2

Answer

0

Answer

2

Answer

3

Question 16

What is the reciprocal of the rational expression: (3x - 2) / (x + 1)?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 17

Simplify the expression (x^2 - 4)/(x - 2).

Accepted Answer

x + 2

Answer

x - 2

Answer

(x + 2)(x - 2)

Answer

(x^2 + 2x + 4)

Question 18

Which of the following is NOT a restriction on the variable x for the rational expression (x - 3)/(x^2 - 9)?

Accepted Answer

x = 1

Answer

x = -3

Answer

x = 3

Answer

x = 0

Question 19

Which of the following rational expressions is undefined when x = 0?

Accepted Answer

(2x)/(x^2 - 1)

Answer

(x + 1)/(x - 2)

Answer

(x - 3)/(x + 3)

Answer

(x^2 + 4)/(x - 1)

Question 20

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

Accepted Answer

x = 2

Answer

x = -2

Answer

x = 3

Answer

x = -3

Question 21

The reciprocal of the rational expression (x - 2)/(x + 3) is:

Accepted Answer

(x + 3)/(x - 2)

Answer

(x - 3)/(x - 2)

Answer

(x - 2)/(x + 3)

Answer

(x + 3)/(x + 2)

Question 22

Which of the following expressions is a rational expression?

Accepted Answer

x / (x - 1)

Answer

2x + 3

Answer

x^2 + 2x - 3

Answer

√(x + 1)

Question 23

Multiply the rational expressions: (x - 1) / (x + 3) * (x + 3) / (x - 2)

Accepted Answer

1

Answer

x - 1

Answer

x - 2

Answer

x + 1

Question 24

Find the inverse of the rational expression: f(x) = (x + 1) / (x - 1)

Accepted Answer

f^-1(x) = (x - 1) / (x + 1)

Answer

f^-1(x) = (x + 1) / (x - 2)

Answer

f^-1(x) = (x - 2) / (x + 1)

Answer

f^-1(x) does not exist

Question 25

What is the result of multiplying (3x)/(x-2) by (x-2)/(5)?

Accepted Answer

3x/5

Answer

x/5

Answer

3/10

Answer

3x²/5

Question 26

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

Accepted Answer

x = 5

Answer

x = 1

Answer

x = 7

Answer

x = 3

Question 27

What is the least common denominator (LCD) of the expressions (x+3)/(x-2) and (x-2)/(x+3)?

Accepted Answer

(x+3)(x-2)

Answer

x²-9

Answer

x+3

Answer

x-2

Question 28

What is the domain of the rational expression (3x-2)/(x²-4)?

Accepted Answer

{x | x ≠ ±2}

Answer

{x | x > -2 and x < 2}

Answer

{x | x ≤ -2 or x ≥ 2}

Answer

All real numbers

Question 29

Which statement is NOT a property of rational expressions?

Accepted Answer

The sum of two rational expressions is always a rational expression.

Answer

A rational expression is undefined when the denominator is 0.

Answer

The quotient of two rational expressions is a rational expression.

Answer

The product of two rational expressions is always a rational expression.

Question 30

Simplify the rational expression: (x² - 4) / (x + 2)

Accepted Answer

x - 2

Answer

x² - 2

Answer

x + 2

Answer

(x - 2)(x + 2)

Question 31

What values of *x* make the rational expression 5 / (x² - 16) undefined?

Accepted Answer

x = 4, x = -4

Answer

x = 4

Answer

x = 16

Answer

x = -4

Question 32

A rectangular garden has a length of (x + 3) meters and a width of (x - 2) meters. What is the area of the garden in terms of *x*?

Accepted Answer

x² + x - 6

Answer

x² - 6

Answer

2x + 1

Answer

x² + 5x + 6

Question 33

A car travels a distance of (x² + 4x) miles in (x + 2) hours. What is the average speed of the car in miles per hour?

Accepted Answer

x

Answer

x² + 2x

Answer

x - 2

Answer

x + 2

Question 34

Simplify the rational expression: (12x²) / (4x)

Accepted Answer

3x

Answer

3 / x

Answer

12x

Answer

3x²

Question 35

What is the simplified form of (x² - 4) / (x + 2)?

Accepted Answer

x - 2

Answer

x + 2

Answer

1 / (x - 2)

Answer

(x - 2)²

Question 36

Multiply the rational expressions: (2x / 3) * (9 / (4x²))

Accepted Answer

3 / (2x)

Answer

(2x²) / 3

Answer

6 / x

Answer

6x

Question 37

Divide the rational expressions: (x² - 9) / (x - 3) ÷ (x + 3) / (2x)

Accepted Answer

2x

Answer

2x / (x - 3)

Answer

2x(x - 3)

Question 38

What is the least common denominator (LCD) of the expressions (2 / (x + 1)) and (5 / (x - 2))?

Accepted Answer

(x + 1)(x - 2)

Answer

x + 1

Answer

x - 2

Answer

(x + 1) + (x - 2)

Question 39

For what value of *x* is the expression (x - 5) / (x + 2) undefined?

Accepted Answer

-2

Answer

-5/2

Answer

5

Answer

0

Question 40

A square has sides of length (x - 2) meters. Find the ratio of its perimeter to its area.

Accepted Answer

4 / (x - 2)

Answer

2 / (x - 2)

Answer

(x - 2) / 4

Answer

(x - 2) / 8

Question 41

Simplify the rational expression: (x^2 - 9) / (x - 3)

Accepted Answer

x + 3

Answer

x - 3

Answer

x^2 - 9

Answer

1

Question 42

If a car travels a distance of (2x + 5y) kilometers in (x + 2y) hours, what is the car's average speed in kilometers per hour?

Accepted Answer

2x + 5y / (x + 2y)

Answer

(2x + 5y)(x + 2y)

Answer

x + 2y

Answer

2x + 5y

Question 43

Divide the rational expression: ((x + 2)/(x - 3)) ÷ ((x - 1)/(x + 1))

Accepted Answer

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

Answer

(x + 1) / (x - 3)

Answer

(x + 2) / (x - 1)

Answer

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

Question 44

Solve the rational equation: (3 / (x - 2)) + (2 / x) = (5x - 1) / (x(x - 2))

Accepted Answer

x = 5

Answer

x = 2

Answer

x = 1

Answer

x = 0

Question 45

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

Accepted Answer

(x + 4) / ((x - 2)(x + 2))

Answer

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

Answer

(x + 2) / (x - 2)

Answer

(x - 2) / (x + 2)

Question 46

Find the sum of the rational expressions: (2 / (x + 1)) + (3 / (x - 1))

Accepted Answer

5x / ((x + 1)(x - 1))

Answer

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

Answer

(x + 3) / (x + 1)

Answer

(x + 2) / (x - 1)

Question 47

A rectangular garden is 5 meters longer than it is wide. If the area of the garden is 24 square meters, what is its length?

Accepted Answer

6 meters

Answer

8 meters

Answer

10 meters

Answer

4 meters

Question 48

Solve the rational inequality: (x + 1) / (x - 2) >= 0

Accepted Answer

x <= -1 or x >= 2

Answer

x < -1 or x > 2

Answer

x > -1 and x < 2

Answer

x <= -2 or x >= 1

Question 49

Simplify the expression: (3x + 6) / (2x - 4) - (x - 2) / (x + 2)

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 50

Determine if the rational expression is in simplest form: (2x + 4)/(x + 2)

Accepted Answer

No

Answer

Yes

Answer

Cannot be determined

Answer

Not applicable

Question 51

Which of the following is a zero of the rational expression: (x - 3)/(x + 1)?

Accepted Answer

x = 3

Answer

x = -1

Answer

x = 1

Answer

x = -3

Question 52

Identify the vertical asymptote of the rational expression: (x^2 - 9)/(x + 3)

Accepted Answer

x = -3

Answer

x = 3

Answer

y = 3

Answer

y = -3