# Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set - Page 516: 41

$\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}=\dfrac{15x-1}{(x+1)^{2}(x-1)}$

#### Work Step by Step

$\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}$ Evaluate the sum of the two rational expressions: $\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}=\dfrac{7(x+1)^{2}+8(x+1)(x-1)}{(x+1)^{3}(x-1)}=...$ Take out common factor $x+1$ from the numerator and simplify: $...=\dfrac{(x+1)[7(x+1)+8(x-1)]}{(x+1)^{3}(x-1)}=\dfrac{7(x+1)+8(x-1)}{(x+1)^{2}(x-1)}=...$ $...=\dfrac{7x+7+8x-8}{(x+1)^{2}(x-1)}=\dfrac{15x-1}{(x+1)^{2}(x-1)}$

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.