Chapter 12.6, Problem 33SR

To determine

To calculate: the sum of expression.

Answer to Problem 33SR

Sum of the expression is $\frac{9h^2-18h}{\left(h+6\right)\left(h-3\right)}$

Explanation of Solution

Given information:

The given expression is $\frac{8h}{h+6}+\frac{h}{h-3}$

Calculation:

The sum of the expression

  $\begin{array}{l}\frac{8h}{h+6}+\frac{h}{h-3}\\ \frac{8h}{h+6}\left(\frac{h-3}{h-3}\right)+\frac{h}{h-3}\left(\frac{h+6}{h+6}\right)\left[\text{write }\frac{8h}{h+6}\text{ and }\frac{h}{h-3}\text{ using LCD,}\left(h+6\right)\left(h-3\right)\right]\\ \frac{8h^2-24h}{\left(h+6\right)\left(h-3\right)}+\frac{h^2+6h}{\left(h+6\right)\left(h-3\right)}\left[\text{simplify}\right]\\ \frac{9h^2-18h}{\left(h+6\right)\left(h-3\right)}\left[\text{add the numerators}\right]\end{array}$

Therefore,

Sum of the expression is $\frac{9h^2-18h}{\left(h+6\right)\left(h-3\right)}$