What is the limit of $(1-x^2)/(x^3-x+1)$ as x approaches infinity?

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Answer 1 · 2016-06-07T01:17:08

We have that

$lim_(x->oo) (1-x^2)/(x^3-x+1)=lim_(x->oo) (x^2*[1/x^2-1])/(x^3*[1-1/x^2+1/x^3])=lim_(x->oo) ([1/x^2-1])/(x*[1-1/x^2+1/x^3])=0$

What is the limit of (1-x^2)/(x^3-x+1)(1-x^2)/(x^3-x+1) as x approaches infinity?