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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 648: 81



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: $$ \frac{x-3}{2\left(x-5\right)}-\frac{3x-5}{\left(x+5\right)\left(x-5\right)}\\ \frac{\left(x-3\right)\left(x+5\right)}{2\left(x-5\right)\left(x+5\right)}-\frac{\left(3x-5\right)\cdot \:2}{\left(x+5\right)\left(x-5\right)\cdot \:2}\\ \frac{\left(x+1\right)\left(x-5\right)}{2\left(x-5\right)\left(x+5\right)}\\ \frac{x+1}{2\left(x+5\right)}$$
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