Q: Find the domain of the rational function $C(x) = \frac{x+9}{x^2-25}$.

$\displaystyle \{ x \mid x \text{ is a real number and } x \neq -5, 5 \}$

Question 1

Which operations require the denominators to be the same before performing the operation on rational expressions?

Accepted Answer

A. Addition and Subtraction

Question 2

Which of the following operations are commutative for real numbers?

Accepted Answer

A. Addition and Multiplication

Question 3

Write $y^{-22}$ with positive exponents.

Accepted Answer

$\displaystyle \frac{1}{y^{22}}$

Question 4

Solve for $x$ in the equation $\displaystyle \frac{x-2}{x+5} = \frac{14}{x+5}$.

Accepted Answer

$\displaystyle x = 16$

Question 5

Which of the following best explains the difference between an equation and an expression?

Accepted Answer

A. Equations contain an equals sign and expressions do not.

Question 6

Simplify the rational expression $\displaystyle \frac{9y-18}{5y-10}$.

Accepted Answer

$\displaystyle \frac{9}{5}$

Question 7

Which of the following is a rational expression?

Accepted Answer

$\displaystyle \frac{P}{Q}$, where $P$ and $Q$ are polynomials and $Q 
eq 0$

Question 8

Find the domain of the rational function $C(x) = \frac{x+9}{x^2-25}$.

Accepted Answer

$\displaystyle \{ x \mid x 	ext{ is a real number and } x 
eq -5, 5 \}$

Question 9

Which of the following expressions is equivalent to $\displaystyle \frac{1}{x^2y}$? Select all that apply.

Accepted Answer

B. $\displaystyle \frac{1}{x^2 y}$

Question 10

Solve for $x$ in the equation $\displaystyle \frac{3}{x+4} = \frac{2}{x-4}$.

Accepted Answer

$\displaystyle x = 20$

Question 11

Simplify the expression $7a^{-4}$ with positive exponents.

Accepted Answer

$\displaystyle \frac{7}{a^4}$

Question 12

Which is the least common denominator (LCD) for the equation $\displaystyle \frac{x}{11} = \frac{x}{3}$?

Accepted Answer

D. 33

Question 13

Solve for $U$ in the equation $P = \frac{R-U}{S}$.

Accepted Answer

$\displaystyle U = R - PS$

Question 14

Sally can paint a room in 3 hours, while Steve can paint the same room in 6 hours. How long would it take them to paint the room if they worked together?

Accepted Answer

A. 2 hours

Question 15

Simplify the complex fraction $\displaystyle \frac{9x^2 - y^2}{xy} \div \frac{3}{y} - \frac{1}{x}$.

Accepted Answer

$\displaystyle 3x + y$

Question 16

Does $\displaystyle \frac{x}{x+2}$ simplify to $\displaystyle \frac{1}{2}$? Why or why not?

Accepted Answer

B. No. There are no common factors in the numerator and the denominator.

Question 17

Solve the equation $\displaystyle \frac{x}{2} + 2 = \frac{27}{x}$.

Accepted Answer

$\displaystyle x = -5, 5$

Question 18

Three postal workers can sort a stack of mail in 10, 15, and 30 minutes, respectively. How long does it take them to sort the mail if all three work together?

Accepted Answer

A. 5 minutes

Question 19

Simplify the expression $x^{-1} x^{-2} + y^{-4}$.

Accepted Answer

$\displaystyle \frac{1}{x^3} + \frac{1}{y^4}$

Question 20

Solve the equation $\displaystyle -\frac{1}{x} = \frac{x}{4}$.

Accepted Answer

$\displaystyle x = 2, -2$

Intermediate Algebra Unit 3 Review – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards