Question 1

Which of the following best describes a rational expression?

Accepted Answer

An expression that is the quotient of two polynomials, where the denominator is not zero.

Question 2

What is the domain of the function $$f(x) = \frac{x-1}{2x-6}$$?

Accepted Answer

$$\{ x \mid x 
eq 3 \}$$

Question 3

Evaluate $$\frac{12}{x+3}$$ for $$x = -1.$$

Accepted Answer

$$\frac{12}{2}$$

Question 4

Simplify $$\frac{28}{35} by $$factoring and canceling common factors.

Accepted Answer

$$\frac{4}{5}$$

Question 5

Which value of $$x$$ makes the denominator of $$f(x) = \frac{3}{11-x}$$ zero?

Accepted Answer

$$x = 11$$

Question 6

What is the least common denominator (LCD) of $$\frac{1}{x}$$ and $$\frac{1}{x^2$}$$?

Accepted Answer

$$x^2$$

Question 7

Rewrite $$\frac{5}{x}$$ with a denominator of $$x^2.$$

Accepted Answer

$$\frac{5x}{x^2$}$$

Question 8

Add $$\frac{3}{x}$$ and $$\frac{4}{x}$$ and simplify.

Accepted Answer

$$\frac{7}{x}$$

Question 9

Simplify $$\frac{x^2$-4}{x^2$-x-6}$$ for $$x=2.$$

Accepted Answer

$$\frac{0}{-4}$$

Question 10

Which of the following is NOT a rational expression?

Accepted Answer

$$\sqrt{x}$$

Question 11

If $$h(x) = \frac{x^2$-2x-8}{x^2$-5x+4}$$, what values are excluded from the domain?

Accepted Answer

$$x = 4$$ and $$x = 1$$

Question 12

What is the simplified form of $$\frac{x-5}{3x^2$-15x}$$?

Accepted Answer

$$\frac{1}{3(x-5)}$$

Question 13

Which step is necessary to add $$\frac{7}{x-3}$$ and $$\frac{x+1}{x^2$-9}$$?

Accepted Answer

Rewrite both expressions with the LCD $$x^2-9$

Question 14

Solve the rational equation $$\frac{3}{x} = 6$$ for $$x.$$

Accepted Answer

Question 15

If the solution to a rational equation is equal to the restriction, what is the solution set?

Accepted Answer

No solution

Question 16

Which of the following is an equivalent expression to $$\frac{7 \cdot 4}{7 \cdot 5}$$ after canceling common factors?

Accepted Answer

$$\frac{4}{5}$$

Question 17

What is the LCD for $$\frac{3x+4}{x^2$+7x+20}$$ and $$\frac{5}{x+4}$$?

Accepted Answer

$$x^2+7x+20$

Question 18

Which of the following is a rational function?

Accepted Answer

$$f(x) = \frac{x-1}{2x-6}$$

Question 19

What is the result of evaluating $$\frac{3x}{x^2$+x-6} at$$ $$x = -2$$?

Accepted Answer

$$\frac{-6}{(-2)^2$+(-2)-6}$$

Chapter 6: Rational Expressions – Simplifying, Domains, and Operations

Study Guide - Practice Questions