Find the oblique asymptote for the graph of y = x^3/x^2-x. Help!?

1 Answer
Jim G.
Jul 30, 2017

#y=x+1#

Explanation:

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is the case here.

#"divide the numerator by the denominator"#

#rArry=x^3/(x(x-1))=x^2/(x-1)larr" simplifying"#

#"an alternative method of division using the divisor as"#
#"a factor in the numerator"#

#color(red)(x)(x-1)color(magenta)(+x)#

#=color(red)(x)(x-1)color(red)(+1)(x-1)color(magenta)(+1)#

#rArrx^2/(x-1)=color(red)(x+1)+1/(x-1)#

as #xto+-oo,ytox+1#

#rArry=x+1" is the oblique asymptote"#
graph{x^3/(x^2-x) [-10, 10, -5, 5]}

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