# How do you find all the asymptotes for function  f(x)=(1/(x-10))+(1/(x-20)) ?

Mar 4, 2016

$x = 10$ and $x = 20$ are two vertical asymptotes

#### Explanation:

Simplifying f(x)=1/(x−10)+1/(x−20), we get

$f \left(x\right) = \frac{\left(x - 20\right) + \left(x - 10\right)}{\left(x - 20\right) \left(x - 10\right)} = \frac{2 x - 30}{\left(x - 20\right) \left(x - 10\right)}$

As $x = 20$ and $x = 10$ i.e. $x = 10$ and $x = 20$ make the denominator zero, these two are two vertical asymptotes.

As degree of numerator is less than that of denominator, there is no other asymptote.

graph{(2x-30)/((x-20)(x-10)) [-10, 30, -5, 5]}