Question

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

Answer 1

`"hole at " x=0, " there are no zeros"`

Explanation:

`"factorise and simplify " R(x)`

`R(x)=(3cancel(x))/(cancel(x)(x-2))=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.

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