Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.6 Rational Expressions - A.6 Assess Your Understanding - Page A53: 52

Answer

$ \dfrac{x^4+x^3-x^2+x-1}{x^3(x^2+1)}$

Work Step by Step

Since the least common multiple (LCM) of the denominator is $x^3(x^2+1)$, then we have $$ \frac{x-1}{x^3}+\frac{x}{x^2+1}=\frac{(x-1)(x^2+1)}{x^3(x^2+1)}+\frac{x^4}{x^3(x^2+1)} .$$ Now, since the denominators are the same, then we have $$ \frac{(x-1)(x^2+1)}{x^3(x^2+1)}+\frac{x^4}{x^3(x^2+1)}= \frac{x^4+x^3-x^2+x-1}{x^3(x^2+1)} .$$
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.