# How do you simplify and state the excluded values for (y+5) /( y^2+4y-32)?

Jun 3, 2015

$\frac{y + 5}{{y}^{2} + 4 y - 32} = \frac{y + 5}{\left(y + 8\right) \left(y - 4\right)}$

If you like, you can eliminate $y$ from the numerator, by writing:

$\frac{y + 5}{\left(y + 8\right) \left(y - 4\right)} = \frac{\left(y - 4\right) + 9}{\left(y + 8\right) \left(y - 4\right)}$

$= \frac{1}{y + 8} + \frac{9}{\left(y + 8\right) \left(y - 4\right)}$

or by writing:

$\frac{y + 5}{\left(y + 8\right) \left(y - 4\right)} = \frac{\left(y + 8\right) - 3}{\left(y + 8\right) \left(y - 4\right)}$

$= \frac{1}{y - 4} - \frac{3}{\left(y + 8\right) \left(y - 4\right)}$

In any case, the excluded values are $y = 4$ and $y = - 8$