Question

Simplify the expression$\frac{a^2+2a-15}{a-3}÷\frac{a^2-4}{2}$

Short answer

The simplified value of expression is$\frac{2\left(a+5\right)}{\left(a-2\right)\left(a+2\right)}$

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{a^2+2a-15}{a-3}÷\frac{a^2-4}{2}$

Step 2. Simplify the expression.

The given expression $\frac{a^2+2a-15}{a-3}÷\frac{a^2-4}{2}$is simplified as:

$\begin{array}{c}\frac{a^2+2a-15}{a-3}÷\frac{a^2-4}{2}=\frac{a^2+2a-15}{a-3}\times \frac{2}{a^2-4}\\ =\frac{\left(a+5\right)\left(a-3\right)}{a-3}\times \frac{2}{\left(a-2\right)\left(a+2\right)}\\ =\frac{2\left(a+5\right)}{\left(a-2\right)\left(a+2\right)}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{2\left(a+5\right)}{\left(a-2\right)\left(a+2\right)}$