Question

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

Answer 1

Note that

`(x^2-1)/(x^3 - 2x^2 -x+2)=(x^2 -1)/(x^2 (x-2)-(x-2))=(x^2 -1)/((x^2 -1)(x-2))`

So, for all
`x \\eq \pm 1`,
`f(x)=(1)/(x-2)`.

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