# Finding the Oblique asymptote

• Nov 7th 2012, 01:09 PM
wolfwood
Finding the Oblique asymptote
I have this equation,

3x^2-16x-12 / x+5

I have to find all of the Asymptotes, Since the numerator is larger then the denominator I know that I need to use long division. I also assume since the Denominator is larger I have a OA instead of an HA. When I graph this function it looks similar to a typical transformed X^2 function. After doing the long division I got OA of 3x-31. Does this need to be simplified more? Also, am I thinking of this problem correctly?
• Nov 7th 2012, 03:25 PM
MarkFL
Re: Finding the Oblique asymptote
You have found the correct OA, and no further simplification is necessary, as you have it in slope-intercept form.

Rather than perform division, you may also get the same result by writing:

$y=\frac{3x^2-16x-12}{x+5}=\frac{3(x+5)^2-46(x+5)+143}{x+5}=$

$3(x+5)-46+\frac{143}{x+5}=3x-31+\frac{143}{x+5}$

Although, it is perhaps more straightforward to perform the division.