# 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)) ?

Jun 15, 2018

Vertical asymptote at $x = - 2$

#### Explanation:

$f \left(x\right) = \frac{x \left(x - 3\right) \left({x}^{2} - x\right)}{\left(x + 2\right) \left({x}^{3} - 3 {x}^{2}\right)}$

factor $\left({x}^{2} - x\right)$ and $\left({x}^{3} - 3 {x}^{2}\right)$.

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

Cancel likewise terms.

$f \left(x\right) = \frac{x - 1}{x + 2}$

Vertical asymptote at $x = - 2$ as $f \left(x\right)$ is not defined there.