## Precalculus (6th Edition)

Published by Pearson

# Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises: 22

#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{x^{2}-4}$ Factor the denominator of the fraction on the right side of the equation: $\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{(x-2)(x+2)}$ Multiply the whole equation by $(x-2)(x+2)$: $(x-2)(x+2)\Big[\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{(x-2)(x+2)}\Big]$ $3(x+2)+x-2=12$ Evaluate the indicated operations: $3x+6+x-2=12$ Take all terms without $x$ to the right side of the equation: $3x+x=12-6+2$ Simplify both sides: $4x=8$ Solve for $x$: $x=\dfrac{8}{4}$ $x=2$ The original equation is undefined for $x=2$, so the equation has no solution.

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