Chapter 12.6, Problem 34SR

To determine

To calculate: the sum of expression.

Answer to Problem 34SR

Sum of the expression is $\frac{8k^2-k}{\left(k-3\right)\left(k+2\right)}$

Explanation of Solution

Given information:

The given expression is $\frac{7k}{k-3}+\frac{k}{k+2}$

Calculation:

The sum of the expression

  $\begin{array}{l}\frac{7k}{k-3}+\frac{k}{k+2}\\ \frac{7k}{k-3}\left(\frac{k+2}{k+2}\right)+\frac{k}{k-3}\left(\frac{k-3}{k-3}\right)\left[\text{write }\frac{7k}{k-3}\text{ and }\frac{k}{k+2}\text{ using LCD,}\left(k-3\right)\left(k+2\right)\right]\\ \frac{7k^2+2k}{\left(k-3\right)\left(k+2\right)}+\frac{k^2-3k}{\left(k-3\right)\left(k+2\right)}\left[\text{simplify}\right]\\ \frac{8k^2-k}{\left(k-3\right)\left(k+2\right)}\left[\text{add the numerators}\right]\end{array}$

Therefore,

Sum of the expression is $\frac{8k^2-k}{\left(k-3\right)\left(k+2\right)}$