# How do you find the x intercept of f(x) = (x^2+9x)/(x^2+3x-4)?

Feb 3, 2015

The $x$-intercept is when $y = 0$

So at first, you only have to look at the top half of the equation -- when this is $0$ the whole thing is $0$

Leaves us with ${x}^{2} + 9 x = 0$

This can be re-written: ${x}^{2} + 9 x = x \left(x + 9\right) = 0$

$x = 0 \mathmr{and} \left(x + 9\right) = 0 \to x = - 9$
Check the answers against the numerator (it may not be $0$!)
$x = 0 \to {x}^{2} + 3 x - 4 = - 4$ which is OK
$x = - 9 \to {x}^{2} + 3 x - 4 = 50$ which is also $\ne 0$