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