College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 34


$ \displaystyle \frac{(x+1)(x+2) }{(x-2)(x-1)}$

Work Step by Step

$=\displaystyle \frac{x^{2}+7x+6}{x^{2}+x-6}\div\frac{x^{2}+5x-6}{x^{2}+5x+6}=\frac{x^{2}+7x+6}{x^{2}+x-6}\cdot\frac{x^{2}+5x+6}{x^{2}+5x-6}$ In each trinomial $x^{2}+bx+c$, we search for factors of c whose sum is b: $x^{2}+7x+6$ ... $,\quad $($6$ and $1$)$\quad $factors to $(x+6)(x+1)$ $x^{2}+5x+6$ ... $,\quad $($+2$ and $+3$)$\quad $factors to $(x+2)(x+3)$ $x^{2}+x-6$... $,\quad $($-2$ and $+3$)$\quad $factors to $(x-2)(x+3)$ $x^{2}+5x-6$... $,\quad $($+6$ and $-1$)$\quad $factors to $(x+6)(x-1)$ $=\displaystyle \frac{(x+6)(x+1)(x+2)(x+3)}{(x-2)(x+3)(x+6)(x-1)}$ after canceling $(x+6)$ and $(x+3),$ $=\displaystyle \frac{(x+1)(x+2) }{(x-2)(x-1)}$
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.