# Chapter 9 - Cumulative Review: 14b

$\dfrac{9a+6}{4a-8}$

#### Work Step by Step

The expression $\dfrac{\dfrac{3}{2+a}+\dfrac{6}{2-a}}{\dfrac{5}{a+2}-\dfrac{1}{a-2}}$ simplifies to \begin{array}{l} \dfrac{\dfrac{3}{a+2}-\dfrac{6}{a-2}}{\dfrac{5}{a+2}-\dfrac{1}{a-2}} \\\\= \dfrac{\dfrac{3(a-2)+6(a+2)}{(a+2)(a-2)}}{\dfrac{5(a-2)-1(a+2)}{a+2}} \\\\= \dfrac{3(a-2)+6(a+2)}{5(a-2)-1(a+2)} \\\\= \dfrac{3a-6+6a+12}{5a-10-a-2} \\\\= \dfrac{9a+6}{4a-8} .\end{array}

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