# How do you simplify (10a^2+11a-6) ÷ (16-a^2)/(5a^2+18a-8)?

Dec 26, 2017

$\frac{- \left(5 a - 2\right) \left(10 {a}^{2} + 11 a - 6\right)}{a - 4}$

#### Explanation:

First, rearrange the expression into

$\left(10 {a}^{2} + 11 a - 6\right) \cdot \frac{5 {a}^{2} + 18 a - 8}{16 - {a}^{2}}$

Then factor the second part of the expression

$\left(10 {a}^{2} + 11 a - 6\right) \cdot \frac{\left(5 a - 2\right) \left(a + 4\right)}{\left(4 - a\right) \left(4 + a\right)}$

Notice that $4 + a$ is the same thing as $a + 4$, so you can cancel both terms to get:

$\left(10 {a}^{2} + 11 a - 6\right) \cdot \frac{\left(5 a - 2\right)}{\left(4 - a\right)}$

I like to put my letter variables in front, so I put a negative sign to balance it out, and my final equation becomes

$\frac{- \left(5 a - 2\right) \left(10 {a}^{2} + 11 a - 6\right)}{a - 4}$