# How do you find the domain, identify any horizontal, vertical, and slant (if possible) asymptotes and identify holes, x-intercepts, and y-intercepts for (x^2-25)/(x^2+5x)?

Jun 4, 2015

I'll give you only a partial answer:

The function can be rewritten as:

$= \frac{\left(x - 5\right) \left(x + 5\right)}{x \cdot \left(x + 5\right)}$

We can cancel out the $\left(x + 5\right)$'s
BUT this we only do if $x \ne - 5$
Also $x \ne 0$
(both cases will make the numerator $= 0$)
So $x = 0 \mathmr{and} x = - 5$are points of interest.

The function turns into:
$= \frac{x - 5}{x}$

That (if $x$ gets large enough) will converge to $\frac{x}{x} = 1$
graph{(x^2-25)/(x^2+5x) [-22.82, 22.81, -11.4, 11.42]}