Question 1

Which of the following is a restriction for the rational expression $$\frac{2x-4}{x+5}$$?

Accepted Answer

$$x 
eq -5$$

Question 2

Simplify the rational expression: $$\frac{5x+10}{2x+4}$$

Accepted Answer

Question 3

What is the simplified form of $$\frac{2x^2$+9x+14}{x^2$+7x+10}$$?

Accepted Answer

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

Question 4

Which of the following is the correct LCD for the denominators $$16x^2y^4$ and 56xy^3$?

Accepted Answer

$$112x^2y^4$

Question 5

Multiply and simplify: $$\frac{x^2$-49}{x^2$-14x+49} \cdot \frac{x-7}{x+7}$$

Accepted Answer

$$1$$

Question 6

Divide and simplify: $$\frac{2x^2$-8x}{x^2$-16} \div \frac{x-4}{x+4}$$

Accepted Answer

$$2(x-4)$$

Question 7

Add and simplify: $$\frac{8}{xy} + \frac{9}{y}$$

Accepted Answer

$$\frac{8+9x}{xy}$$

Question 8

Subtract and simplify: $$\frac{5}{x-3} - \frac{6}{2(x-3)}$$

Accepted Answer

$$\frac{4}{2(x-3)}$$

Question 9

Solve for $$x$$: $$\frac{1}{5x} + \frac{2}{3x} = 1$$

Accepted Answer

$$x = \frac{8}{15}$$

Question 10

If $$\frac{1}{f} = \frac{1}{a} + \frac{1}{b}$$, solve for $$a in $$terms of $$f$$ and $$b.$$

Accepted Answer

$$a = \frac{bf}{b-f}$$

Question 11

The gravitational force $$F$$ between two masses $$m_1$$ and $$m_2 a $$distance $$d$$ apart is $$F = \frac{Gm_1m_2}{d^2$}. $$Solve for $$m_2.$$

Accepted Answer

$$m_2$$ = \frac{$$Fd^2$$}{$$Gm_1$$}$$

Question 12

Janice can complete a task in 4 hours, Marie in 3 hours. Working together, how long will it take them to complete the task?

Accepted Answer

$$\frac{12}{7}$$ hours

Question 13

Which of the following is a complex rational expression?

Accepted Answer

$$\frac{\frac{2}{x}}{\frac{3}{y}}$$

Question 14

Simplify the complex rational expression: $$\frac{\frac{1}{x} + \frac{2}{y}}{\frac{1}{x}}$$

Accepted Answer

$$1 + \frac{2x}{y}$$

Question 15

Terry drove 360 km at a speed 20 km/h faster than Kathy, who drove 280 km. If their travel times were equal, what was Kathy's speed?

Accepted Answer

$$70 km/h$$

Question 16

Given similar triangles with sides 17, 14 and 23, $$y$$, and $$\frac{17}{14} = \frac{23}{y}$$, what is $$y$$?

Accepted Answer

$$\frac{322}{14}$$

Intermediate Algebra: Rational Expressions and Functions

Study Guide - Practice Questions