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

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