# How do you find vertical, horizontal and oblique asymptotes for  x / (3x(x-1))?

May 6, 2016

There is a vertical asymptote at $x = 1$ and a horizontal asymptote at $y = 0$

#### Explanation:

To find all the asymptotes for function $y = \frac{x}{3 x \left(x - 1\right)}$, we first observe that $x$ cancels out from numerator and denominator and the function is primarily $\frac{x}{3 \left(x - 1\right)}$, but there is a hole at $x = 0$

Let us first start with vertical asymptotes, which are given by putting denominator equal to zero or $x - 1 = 0$ i.e. $x = 1$.

Further as in $y = \frac{3}{x - 1}$, there is no variable in numerator, we have a horizontal asymptote at $y = 0$

graph{x/(3x(x-1)) [-10, 10, -5, 5]}