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Find an equation of the slant asymptote. Do not sketch the curve.

$ y = \dfrac{2x^3 - 5x^2 + 3x}{x^2 - x - 2} $

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Missouri State University

Campbell University

University of Nottingham

Idaho State University

So the quotient of our polynomial division is going to be the equation for these slant ask himto. So, um, how many times can x square to go into two x cubed two x So two x times x squared We're gonna multiply this by every single term and change the sign because we want the 1st 1 to cancel out. So, um, we get minus two x cubed two x times negative X is two x squared negative two x squared. But we wanted to be positive because we're switching all the signs. So plus two x squared and then the last term sort to sign minus for X racing ideas to cancel out And we're left with minus three x squared minus X. So we're going to do so now we're going to do our next term. How many times can x squared going to minus three x squared? So that's minus three minus three times x squared trains The sign plus three X squared minus three X minus six and we're left with minus four X minus six. And this can. Now this one's power is greater than this. So we're done. This is our quotient. So that's the equation. Why equals two X minus three is the equation for the slants ass in tow