Question

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

Answer 1

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+9x=0`

This can be re-written: `x^2+9x=x(x+9)=0`

So we have two answers:
`x=0 or (x+9)=0->x=-9`

Check the answers against the numerator (it may not be `0`!)
`x=0->x^2+3x-4=-4` which is OK
`x=-9->x^2+3x-4=50` which is also `!=0`