sombereki51

2022-09-23

How do you find the x intercept of $f\left(x\right)=\frac{{x}^{2}+9x}{{x}^{2}+3x-4}$?

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Miguel Shah

Expert

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: ${x}^{2}+9x=x\left(x+9\right)=0$

$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\left(x+9\right)=0\to x=-9$

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

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