# How do you find the zeros and holes, if any, of R( x) = (3x)/(x^2 - 2x)?

Apr 22, 2017

$\text{hole at " x=0, " there are no zeros}$

#### Explanation:

$\text{factorise and simplify } R \left(x\right)$

$R \left(x\right) = \frac{3 \cancel{x}}{\cancel{x} \left(x - 2\right)} = \frac{3}{x - 2}$

Since we have removed a factor of x, this indicates there is a hole at x=0

Zeros are the values of x that make R(x) equal zero.

This occurs when the numerator is zero.

$\text{Since the numerator is 3 there are no zeros}$
graph{(3x)/(x^2-2x) [-10, 10, -5, 5]}