# How do you find the slant asymptote of #y=(x^2+12)/(x-2)#?

##### 1 Answer

The slant asymptote is

#### Explanation:

Given:

The slant asymptote occurs when the degree in the numerator is one greater than the degree in the denominator.

Since the denominator is a linear factor, you can use either long division or synthetic division to find the slant asymptote.

**Using long division:**

First set up the divisor and dividend as follows. Make sure the dividend has a term for each degree even if it is zero. Select

Subtract and bring down the next monomial in the dividend:

What monomial can we add to the quotient that will eliminate the

Multiply this monomial in the quotient by each monomial in the divisor, then subtract:

The slant asymptote is