Question

Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2​

Answer 1

Note that

$\frac{x^2-1}{x^3 - 2x^2 -x+2}=\frac{x^2 -1}{x^2 (x-2)-(x-2)}=\frac{x^2 -1}{(x^2 -1)(x-2)}$

So, for all $x \neq \pm 1$, $f(x)=\frac{1}{x-2}$.

So, the graph looks like something like as following in the image.