What are the asymptote(s) and hole(s), if any, of # f(x) =((x-3)/(x+2)x)((x^2-x)/(x^3-3x^2)) #?

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Answer 1 · 2018-06-15T18:13:38

Vertical asymptote at #x=-2#

#f(x)={x(x-3)(x^2-x)}/{(x+2)(x^3-3x^2)}#

factor #(x^2-x)# and #(x^3-3x^2)#.

#f(x)={x^2(x-3)(x-1)}/{x^2(x+2)(x-3)}#

Cancel likewise terms.

#f(x)={x-1}/{x+2}#

Vertical asymptote at #x=-2# as #f(x)# is not defined there.

What are the asymptote(s) and hole(s), if any, of # f(x) =((x-3)/(x+2)*x)*((x^2-x)/(x^3-3x^2)) #?