# How do you find the asymptotes for #(x^2 + x + 3 )/( x-1)#?

##### 1 Answer

Jun 21, 2016

Vertical asymptote

Oblique asymptote

#### Explanation:

#f(x) = (x^2+x+3)/(x-1)#

#= (x^2-x+2x-2+5)/(x-1)#

#= ((x+2)(x-1)+5)/(x-1)#

#= x+2+5/(x-1)#

As

So there is an oblique (slant) asymptote

When

graph{(y - (x^2+x+3)/(x-1))(y - (x+2)) = 0 [-39, 41, -17.04, 22.96]}