# How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x) = ((x – 10)(x + 5) )/( (13x + 10)(10–x))#?

##### 1 Answer

The vertical asymptote is

#### Explanation:

First notice that

(Since that factor reduces out we know that the function has a removable discontinuity--or hole--at x = 10, but that wasn't asked.)

Now, vertical asymptotes are the zeros of the factors of the denominator that do not cancel with factors of the numerator, so in this case a vertical asymptote is at

Horizontal asymptotes are the ratio of the leading coefficients of the numerator and denominator if both the numerator and denominator have the same degree (which they do in this case).

The horizontal asymptote in this case is