# How do you find the slant asymptote of #(x^2)/(x-3)#?

##### 1 Answer

Dec 27, 2015

Divide the numerator

#### Explanation:

You can divide the polynomials in several different ways.

Here's a long division of the coefficients:

Note the

Equivalently, you can add and subtract terms to separate out multiples of the divisor like this:

#x^2/(x-3)#

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

#=(x(x-3)+3x)/(x-3)#

#=x + (3x)/(x-3)#

#=x + (3x-9+9)/(x-3)#

#=x + (3(x-3)+9)/(x-3)#

#=x + 3 + 9/(x-3)#

In either case, we find that the quotient is

As

#y = x+3#