# How do you simplify (2x^2+6x+4)/(4x^-12x-16)?

Jul 5, 2015

I will assume the expression in the question should be

$\frac{2 {x}^{2} + 6 x + 4}{4 {x}^{2} - 12 x - 16} = \frac{x + 2}{2 \left(x - 4\right)}$

with exclusion $x \ne - 1$

#### Explanation:

$\frac{2 {x}^{2} + 6 x + 4}{4 {x}^{2} - 12 x - 16}$

$= \frac{2 \left({x}^{2} + 3 x + 2\right)}{4 \left({x}^{2} - 3 x - 4\right)}$

$= \frac{2 \left(x + 1\right) \left(x + 2\right)}{4 \left(x + 1\right) \left(x - 4\right)}$

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

with exclusion $x \ne - 1$

If $x = - 1$ the original expression becomes $\frac{0}{0}$ which is not defined.