# How do you find the slant asymptote of #(x^2+3x-4)/x#?

##### 1 Answer

Divide the expressions and discard the remainder.

#### Explanation:

Ok, so the slant asymptote means that as x gets infinitely big, the graph gets closer to a particular line, which is the slant asymptote. So you divide the numerator by the denominator, and, assuming it's ( **ignore any remainder** , then you should get a line equation y=mx+b. That line is your slant asymptote.

In this case you can divide all numerator terms by x, so

Please note that slant asymptotes only occur when the degree (highest exponent) in the numerator is exactly one more than the denominator, in this case 2 & 1. Also note that in a more complicated case, as if you had say (x+1) in the denominator, then you'd have to use long or synthetic division to get the asymptote.