Question

Simplify the expression$\frac{a}{a^2-a-20}+\frac{2}{a+4}$.

Short answer

The simplified value of expression is$\frac{3a-10}{\left(a-5\right)\left(a+4\right)}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{a}{a^2-a-20}+\frac{2}{a+4}$.

Step 2. Simplify the expression.

The given expression $\frac{a}{a^2-a-20}+\frac{2}{a+4}$is simplified as:

$\begin{array}{c}\frac{a}{a^2-a-20}+\frac{2}{a+4}=\frac{a}{\left(a-5\right)\left(a+4\right)}+\frac{2}{a+4}\\ =\frac{a+2\left(a-5\right)}{\left(a-5\right)\left(a+4\right)}\\ =\frac{3a-10}{\left(a-5\right)\left(a+4\right)}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{3a-10}{\left(a-5\right)\left(a+4\right)}$.