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

1 Answer
Apr 22, 2017

Answer:

#"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]}