Does (3x^4 + 5x +1)/(1+x^2) have a slant asymptote?

Question

solomonzelman · Answer

Do long division.

solomonzelman · Answer

I would reorder before you do long division. Switch places  "x^2" and "1"
Say it is (3x^4 + 5x +1)/(x^2+1)
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DIVIDE.

solomonzelman · Answer

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anonymous · Answer

I thought the difference in degree cannot be more than 1 for there to be a slant asymptote?

solomonzelman · Answer

Hold on, what did you get when you divided?

solomonzelman · Answer

It can be (not in your case, just for example)
y=x+4 or something like that.

solomonzelman · Answer

I am not really good at explaining, if you didn't understand my bad explananion, you can always refer to this http://www.purplemath.com/modules/asymtote3.htm It's a good website to visit.

anonymous · Answer

When I divided, I got 3x^2-3, but I'm not sure that's the answer since some websites say that for the slant asymptote to exist, the difference in degree between the numerator and denominator cannot be greater than 1?

hero · Answer

Yes, this is true. Also, if you graph the function, you get this: https://www.desmos.com/calculator/alosfnhblk