Question 1

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

Accepted Answer

Multiply both sides by $$x to $$eliminate denominators.

Question 2

After multiplying both sides of $$\frac{x^2$ - 3}{x} - 2 = \frac{3(x-1)}{x} by$$ $$x$$, what is the resulting equation?

Accepted Answer

$$x^2 - 3 - 2x = 3(x-1$$)$$

Question 3

Solve for $$x in $$the equation $$x^2 - 3 - 2x = 3(x-1$$)$$. What is the solution?

Accepted Answer

$$x = 3$$

Question 4

Which value must be excluded from the solution set of $$\frac{x^2$ - 3}{x} - 2 = \frac{3(x-1)}{x}$$?

Accepted Answer

$$x = 0$$

Question 5

Given the equation $$p^{-2}$$ + $$2p^{-1} - 3 = 0$, which is the correct form using only positive exponents?

Accepted Answer

$$\frac{1}{p^2$} + \frac{2}{p} - 3 = 0$$

Question 6

What is the least common denominator (LCD) for the equation $$\frac{1}{p^2$} + \frac{2}{p} - 3 = 0$$?

Accepted Answer

$$p^2$$

Question 7

After multiplying both sides of $$\frac{1}{p^2$} + \frac{2}{p} - 3 = 0 by $$the LCD, what is the resulting equation?

Accepted Answer

$$1 + 2p - 3p^2$ = 0$$

Question 8

Solve $$1 + 2p - 3p^2$ = 0$$ for $$p. $$Which of the following is a solution?

Accepted Answer

$$p = 1$$

Question 9

Which step is essential after finding solutions to a rational equation?

Accepted Answer

Check each solution in the original equation to avoid extraneous solutions.

Question 10

A chemical reaction is modeled by $$\frac{c^2$ - 4}{c} = 2. $$What is the value of $$c$$?

Accepted Answer

$$c = 4$$

Question 11

Which of the following best describes why $$x = 0 is $$not a solution to $$\frac{x^2$ - 3}{x} - 2 = \frac{3(x-1)}{x}$$?

Accepted Answer

It makes the denominator zero, causing division by zero.

Question 12

If a rational equation has a solution that makes any denominator zero, what should you do?

Accepted Answer

Exclude that solution from the solution set.

Question 13

Which of the following is a multi-step process for solving rational equations?

Accepted Answer

Multiply both sides by the LCD, simplify, solve, and check solutions.

Question 14

A medical dosage formula is given by $$\frac{d^2$ - 9}{d} = 0. $$What is the correct value for $$d$$?

Accepted Answer

$$d = 3$$

Question 15

Which of the following is a common mistake when solving rational equations?

Accepted Answer

Forgetting to check for extraneous solutions.

Intermediate Algebra Study Guide: Solving Rational Equations and Exponents

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