What is the equation of the oblique asymptote $f(x)=(x^2-x-2)/(x+1)$ ?

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Answer 1 · 2015-07-18T10:22:20

$f(x) = (x^2-x-2)/(x+1) = ((x-2)(x+1))/(x+1) = x-2$

So $f(x)$ is a straight line (with excluded point $(-1,-3)$ ).

It has no asymptote.

$(x^2-x-2)/(x+1)$

$= (x^2+x-2x-2)/(x+1)$

$= (x(x+1)-2(x+1))/(x+1)$

$= ((x-2)(x+1))/(x+1) = x-2$

with exclusion $x != -1$

What is the equation of the oblique asymptote f(x)=(x^2-x-2)/(x+1)f(x)=(x^2-x-2)/(x+1)?