# How do you simplify and find the excluded values of #(v^2+4) / (v^2-3v-18)#?

##### 1 Answer

Asymptote at

#### Explanation:

Excluded values mean asymptotes and holes. So let's look for them:

First, let's expand all our components:

The numerator almost looks like a *differnce of squares*, but it's adding instead of subtracting. That means that the expanded version of it will have imaginary numbers (

The denominator is easier. We just need to factor.

We are looking for two numbers that **add** to

To find the factors, let's ignore the signs for now:

........................

Now we have our factors:

Asymptotes are values of

**Case 1**

**Case 2**

So, when

there are no holes (no identical factors in the numerator and denominator), so the only excluded values are

Just to check our work, let's graph the equation and see

graph{y=(x^2+4)/((x-6)(x+3))}