Question 1

Which value of $x$ must be excluded from the solution set of the equation $\frac{8}{3x+2} - \frac{1}{x-7} = 0$?

Accepted Answer

$x = -\frac{2}{3},\ 7$

Question 2

For the equation $\frac{1}{x-4} + \frac{1}{x+1} = \frac{1}{x^2-3x-4}$, which values of $x$ are not allowed?

Accepted Answer

$x = 4,\ -1$

Question 3

Solve the equation $\frac{2x+4}{2} - \frac{3x}{x-2} = x$. What is the solution set?

Accepted Answer

$\{-4\}$

Question 4

Solve the equation $\frac{6}{x^2-1} - \frac{3}{x-1} = \frac{7}{x+1}$. What is the solution set?

Accepted Answer

The solution set is empty.

Question 5

Solve the equation $\frac{2x+1}{x-2} + \frac{4}{x} = \frac{-8}{x^2-2x}$. What is the solution set?

Accepted Answer

$\left\{-\frac{5}{2}\right\}$

Question 6

Solve the equation $4 = \frac{7}{4x-3} - \frac{3}{(4x-3)^2}$. What is the solution set?

Accepted Answer

$\left\{\frac{15}{16},\ 1\right\}$

Question 7

Solve the equation $x - \sqrt{35-2x} = 0$. What is the solution set?

Accepted Answer

$\{5\}$

Question 8

Solve the equation $\sqrt{7x-6} - 1 = 3x - 23$. What is the solution set?

Accepted Answer

$\{10\}$

Question 9

Solve the equation $\sqrt{4y+20} - \sqrt{y-4} = 6$. What is the solution set?

Accepted Answer

$\{4,\ 20\}$

Question 10

Solve the equation $\sqrt{3x} = \sqrt{7x+16} - 4$. What is the solution set?

Accepted Answer

$\{0,\ 12\}$

Question 11

Solve the equation $(x-4)^{2/3} = 4$. What is the solution set?

Accepted Answer

$\{-4,\ 12\}$

Question 12

Solve the equation $(2x-3)^{2/3} = x^{1/3}$. What is the solution set?

Accepted Answer

$\left\{1,\ \frac{9}{4}\right\}$

Question 13

Solve the equation $15x^4 - 14x^2 + 3 = 0$. What is the solution set?

Accepted Answer

$\left\{\frac{\sqrt{15}}{5},\ -\frac{\sqrt{15}}{5},\ \frac{\sqrt{3}}{3},\ -\frac{\sqrt{3}}{3}\right\}$

Question 14

Solve the equation $(x-1)^{2/3} + (x-1)^{1/3} - 20 = 0$. What is the solution set?

Accepted Answer

$\{-124,\ 65\}$

Question 15

Solve the equation $15(x^2)^2 - 23(x^2) + 2 = -4$. What is the solution set?

Accepted Answer

$\left\{\frac{2\sqrt{3}}{3},\ -\frac{2\sqrt{3}}{3},\ \frac{\sqrt{5}}{5},\ -\frac{\sqrt{5}}{5}\right\}$

College Algebra Study Guide: Rational and Radical Equations

Study Guide - Practice Questions