Chapter 9, Problem 8MS

To determine

To Simplify: The expression and assume that no denominator is zero.

Answer to Problem 8MS

  $-\frac{y+1}{2(y-7)}$

Explanation of Solution

Given: $\frac{y^2+12y+36}{36-y^2}\cdot \frac{y^2-5y-6}{2y^2-2y-84}$

Given: $\frac{y^2+12y+36}{36-y^2}\cdot \frac{y^2-5y-6}{2y^2-2y-84}$

Factoring and then solving

  $\begin{array}{l}=\frac{y^2+12y+36}{36-y^2}\times \frac{y^2-5y-6}{2y-2y-84}\\ =\frac{(y+6)(y+6)}{-(y+6)(y-6)}\times \frac{(y-6)(y+1)}{2(y-7)(y+6)}\\ =-\frac{y+1}{2(y-7)}\end{array}$

Hence, $-\frac{y+1}{2(y-7)}$