Question 1

Which of the following is a rational expression?

Accepted Answer

$$\frac{2x + 1}{x - 5}$$

Question 2

Find the domain of the rational function $$f(x) = \frac{3x + 2}{x^2$ - 4}.$$

Accepted Answer

$$x 
eq 2,\ x 
eq -2$$

Question 3

Simplify the rational expression: $$\frac{2x^2$ - 11x - 21}{x^2$ - 8x + 7}.$$

Accepted Answer

$$\frac{2x + 3}{x - 7}$$

Question 4

Which of the following is NOT a step in simplifying a rational expression?

Accepted Answer

Remove common terms from numerator and denominator

Question 5

Multiply and simplify: $$\frac{x^2$ - 9}{x^2$ - x - 6} 	imes \frac{x - 2}{x + 3}.$$

Accepted Answer

$$\frac{x - 3}{x + 2}$$

Question 6

Divide and simplify: $$\frac{a + b}{ab} \div \frac{a^2$ - b^2$}{2a^3$b}.$$

Accepted Answer

$$\frac{2}{a^2$}$$

Question 7

Find the area of a rectangle with length $$\frac{2x}{x^2$ - 81}$$ and width $$\frac{x + 9}{x}.$$

Accepted Answer

$$\frac{2}{x - 9}$$

Question 8

Which value of $$x$$ makes the rational expression $$\frac{5x}{x^2$ - 25}$$ undefined?

Accepted Answer

$$x = 5 or$$ $$x = -5$$

Question 9

Simplify: $$\frac{x^2$ - 16}{x^2$ + 8x + 16}.$$

Accepted Answer

$$\frac{x - 4}{x + 4}$$

Question 10

A company’s cost per disc for pressing $$x$$ compact discs is given by $$C(x) = \frac{500 + 2x}{x}. $$What is the cost per disc for pressing 100 discs?

Accepted Answer

$$7$$

Question 11

Which of the following is equivalent to $$\frac{1}{x} + \frac{2}{x}$$?

Accepted Answer

$$\frac{3}{x}$$

Question 12

Which of the following is a correct step in simplifying $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

Factor numerator and denominator

Question 13

If $$f(x) = \frac{4x}{x^2$ - 1}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 1,\ x 
eq -1$$

Question 14

Which of the following is a real-world application of rational expressions?

Accepted Answer

Calculating the average speed of a car over a trip with varying speeds

Question 15

Simplify: $$\frac{3x^2$ - 12}{6x}.$$

Accepted Answer

$$\frac{x - 2}{2}$$

Intermediate Algebra Study Guide: Rational Expressions and Functions

Study Guide - Practice Questions

Study Guide - Flashcards