Chapter 11.8, Problem 14MRE

To determine

To find: The solution of the given expression.

Answer to Problem 14MRE

The solution of the given expression is $b=-2$ .

Explanation of Solution

Given information:

The given equation is,

  $\frac{4}{b+6}=\frac{-1}{2b+3}$

The solution of the given expression is obtained as,

  $\begin{array}{l}\frac{4}{b+6}=\frac{-1}{2b+3}\\ \frac{4}{b+6}+\frac{1}{2b+3}=0\\ \frac{4\left(2b+3\right)+\left(b+6\right)}{\left(b+6\right)\left(2b+3\right)}=0\\ 8b+12+b+6=0\end{array}$

Simplify further,

  $\begin{array}{l}9b+18=0\\ 9b=-18\\ b=-2\end{array}$

Thus, the solution of the given expression is $b=-2$ .