## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 8 Rational Functions - 8.6 Solve Rational Equations - Guided Practice for Examples 3, 4, and 5 - Page 591: 8

#### Answer

$$x=-3$$

#### Work Step by Step

In order to solve this equation, we find the common denominator of the two fractions. However, instead of trying to combine the fractions, we multiply both sides of the equation by this denominator. Doing this, we find: $$\frac{3}{2}\cdot \:2\left(x-1\right)+\frac{4}{x-1}\cdot \:2\left(x-1\right)=\frac{x+1}{x-1}\cdot \:2\left(x-1\right) \\ 3\left(x-1\right)+8=2\left(x+1\right)\\ x=-3$$ Checking, we see that the solution is not extraneous.

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