How do you find the slant asymptote of #(x^2+3x+2)/(x-2)#?

1 Answer
George C.
Dec 27, 2015

Divide to find the quotient polynomial #y = x+5#, which is the slant asymptote (otherwise known as the oblique asymptote).

Explanation:

Long divide or do something like this to separate out the quotient #(x+5)# and remainder #12#:

#(x^2+3x+2)/(x-2)#

#=(x^2-2x+5x-10+12)/(x-2)#

#=((x^2-2x)+(5x-10)+12)/(x-2)#

#=(x(x-2)+5(x-2)+12)/(x-2)#

#=((x+5)(x-2)+12)/(x-2)#

#=x+5 + 12/(x-2)#

Then as #x->+-oo# the term #12/(x-2) -> 0#

So the slant asymptote is #y = x+5#

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