# Chapter 9 - Section 9.5 - Logarithmic Functions - Exercise Set - Page 572: 90

$\dfrac{y-9}{(y+1)(y-1)}$

#### Work Step by Step

Using the $LCD= (y+1)(y-1)$, the given rational expression, $\dfrac{5}{y+1}-\dfrac{4}{y-1} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{(y-1)(5)-(y+1)(4)}{(y+1)(y-1)} \\\\= \dfrac{5y-5-4y-4}{(y+1)(y-1)} \\\\= \dfrac{y-9}{(y+1)(y-1)} .\end{array}

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