# How do you identify all asymptotes or holes for #f(x)=(x^2-5x+6)/(x^2-4x+3)#?

##### 1 Answer

Dec 10, 2016

There is a hole at

The vertical asymptote is

The horizontal asymptote is

#### Explanation:

Let's factorise the numerator and denominator

So,

So, there is a hole at

The domain of

As we cannot divide by

So, the vertical asymptote is

To calculate the limits as

So, the horizontal asymptote is

graph{(y-(x-2)/(x-1))(y-1)=0 [-11.25, 11.25, -5.625, 5.625]}