Multiply both sides by $$3(x-1)$$ where $$x \neq 1$$

Question 1

Which of the following is the correct first step to solve the rational equation $$\frac{2}{x-1} = \frac{3}{3}$$?

Accepted Answer

Multiply both sides by $$3(x-1)$$ where $$x 
eq 1$$

Question 2

A rational equation has a solution $$x = 2$$, but substituting $$x = 2$$ makes a denominator zero. What should you do?

Accepted Answer

Exclude $$x = 2$$ from the solution set

Question 3

Solve the equation $$\frac{1}{x} + \frac{1}{x-2} = 1$$ for $$x.$$

Accepted Answer

$$x = 1 or$$ $$x = -1$$

Question 4

If a machine can complete a task in $$t$$ hours, what is its rate of work per hour?

Accepted Answer

$$1/t$$

Question 5

Two workers can complete a job together in 4 hours. Worker A alone takes 6 hours. How long does Worker B take alone?

Accepted Answer

12 hours

Question 6

Solve the equation $$\sqrt{x+1} = x-1.$$

Accepted Answer

$$x = 3$$

Question 7

Which of the following is a valid step when solving $$\sqrt{x+2} + \sqrt{x-1} = 3$$?

Accepted Answer

Isolate one radical before squaring

Question 8

Solve the equation $$x^{2/3} = 16$.

Accepted Answer

$$x = 64$$

Question 9

Which of the following equations is quadratic in form?

Accepted Answer

$$x^4$$ - $$5x^2 + 6 = 0$

Question 10

Solve the equation $$x^{1/2} - 5 = 0$.

Accepted Answer

$$x = 25$$

Question 11

If $$\sqrt{x+3} = x - 1$$, what must you do after squaring both sides?

Accepted Answer

Check for extraneous solutions

Question 12

Which of the following is the correct solution set for $$x^4$$ - $$5x^2 + 4 = 0$?

Accepted Answer

$$\{2, -2\}$$

Question 13

A plumber can fix a leak in 3 hours, and an apprentice can do it in 6 hours. How long will it take them working together?

Accepted Answer

2 hours

Question 14

Solve the equation $$\sqrt{2x+3} = 5.$$

Accepted Answer

$$x = 11$$

Question 15

Which of the following is a necessary restriction when solving $$\frac{1}{x-2} = 3$$?

Accepted Answer

$$x 
eq 2$$

Question 16

Solve the equation $$x^{3/2} = 27$.

Accepted Answer

$$x = 9$$

Question 17

Which of the following is the correct solution set for $$x^2 - 4x + 4 = 0$?

Accepted Answer

$$\{2\}$$

Question 18

If $$x^{1/3} = 8$, what is x$?

Accepted Answer

$$x = 512$$

Question 19

Which of the following is a correct application of the zero-factor property?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0$$

Solving Rational, Radical, and Quadratic-in-Form Equations in College Algebra

Study Guide - Practice Questions