### 4.5 Slant Asymptotes

I was having trouble editing my other post, so i created a new one for the stuff we learned today dealing with slant asymptotes. If you're like me, you never learned about long division involving a variable. Its very similar to normal long division.

First, I'll tell you about the application of long division. In rational functions,

*slant asymptotes*occur when the degree(highest exponent) of the numerator is one larger than the degree of the denominator. A slant asymptote is a linear function (following the form y =mx + b) that is never reached by the function.

So a function can have no vertical or horizontal asymptotes, but it might have a slant asymptote.

To find the slant asymptote, use long division. For example: ( 2 - 3x^2)/(x-1)

start by setting the equation up as a normal long division problem.

to learn how to do long division go to this very helpful site (they explain it better than i can): http://www.purplemath.com/modules/polydiv2.htm

the result is -3x-3 + (-1/(x-1))

you only use the -3x-3 part of this because the rest is a remainder.

Therefore, the slant asymptote is y = -3x - 3

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