## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 6 - Rational Expressions and Equations - 6.4 Addition and Subtraction with Unlike Denominators - 6.4 Exercise Set - Page 401: 46

#### Answer

$$\frac{x-3}{\left(x+3\right)\left(x+1\right)}$$

#### Work Step by Step

In order to add or subtract fractions, we must first make sure that the denominators are the same. After we create like denominators, we combine the numerators together to get the new fraction. Doing this, we find: $$\frac{x}{\left(x+2\right)\left(x+3\right)}-\frac{2}{\left(x+1\right)\left(x+2\right)}\\ \frac{x\left(x+1\right)}{\left(x+2\right)\left(x+3\right)\left(x+1\right)}-\frac{2\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}\\ \frac{\left(x+2\right)\left(x-3\right)}{\left(x+2\right)\left(x+3\right)\left(x+1\right)}\\ \frac{x-3}{\left(x+3\right)\left(x+1\right)}$$

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