Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 43

Answer

$\frac{2x+5}{(x+1)(x+2)}$

Work Step by Step

$\frac{3}{x+1}-\frac{1}{x+2}$ Find the lowest common denominator (i.e. $(x+2)(x+1)$) and adjust the fractions accordingly: $=\frac{3\times (x+2)}{(x+1)(x+2)}-\frac{1\times (x+1)}{(x+1)(x+2)}$ Expand any brackets: $=\frac{3x+6}{(x+1)(x+2)}-\frac{x+1}{(x+1)(x+2)}$ Combine the fractions: $=\frac{3x+6-(x+1)}{(x+1)(x+2)}$ Expand the negative sign: $=\frac{3x+6-x-1}{(x+1)(x+2)}$ Collect the like terms: $=\frac{2x+5}{(x+1)(x+2)}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.