# How do you simplify (b^2+2b-24)/(2b^2-72) and find any non permissible values?

Oct 23, 2016

The expression simplifies to $\frac{b - 4}{2 \left(b - 6\right)}$, $b \ne - 6 , 6$.

#### Explanation:

Factor everything.

$= \frac{\left(b + 6\right) \left(b - 4\right)}{2 \left({b}^{2} - 36\right)}$

$= \frac{\left(b + 6\right) \left(b - 4\right)}{2 \left(b + 6\right) \left(b - 6\right)}$

$= \frac{b - 4}{2 \left(b - 6\right)}$

For the non-permissible values, these will occur when the denominator equals $0$.

$0 = 2 {b}^{2} - 72$

$0 = 2 \left({b}^{2} - 36\right)$

$0 = \left(b + 6\right) \left(b - 6\right)$

$b = - 6 \mathmr{and} 6$

Hopefully this helps!