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 $$\displaystyle \frac{1}{x^2$y}$$? 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

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