# What's the domain of g(x)=(x^2-5x+4)/(x^2-2x-15)?

$x \ne 5 , - 3$

#### Explanation:

We have the function:

$g \left(x\right) = \frac{{x}^{2} - 5 x + 4}{{x}^{2} - 2 x - 15}$

Let's first talk about the values of $x$ that won't be allowed in the domain. Why would an $x$ value be disallowed?

In this case, when dealing with a fraction, we can't have the denominator be 0. So what values of $x$ will make the denominator 0?

We can find that by saying:

${x}^{2} - 2 x - 15 = 0$

and now solving for $x$:

$\left(x - 5\right) \left(x + 3\right) = 0$

$x = 5 , - 3$

And so these are the two values that aren't allowed.

We can see that in the graph:

graph{(x^2-5x+4)/(x^2-2x-15) [-33.28, 39.8, -13.83, 22.75]}

(If you scroll on the graph, you can zoom in on those two $x$ values to see they are disallowed).