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

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Answer 1 · 2015-11-19T23:57:10

$y = x$ $y = x$

$f (x) = \frac{x^{2} + x - 2}{x + 1} = \frac{x (x + 1) - 2}{x + 1} = x - \frac{2}{x + 1}$ $f(x)=(x^2+x-2)/(x+1) = (x(x+1)-2)/(x+1) = x-2/(x+1)$

As $x \to \pm \infty$ $x->+-oo$ we have $- \frac{2}{x + 1} \to 0$ $-2/(x+1) -> 0$ .

So $f (x)$ $f(x)$ has an oblique asymptote with equation $y = x$ $y = x$

What is the equation of the oblique asymptote f(x)=x2+x−2x+1 f(x) = (x^2+x-2)/(x+1)?