Question

For which values of x will the rational expression below be equal to zero?

(X-1)(x+5)/(x-5)

Answer 1

1 and -5

Explanation:

0 divided by anything is 0

the numerator can equal zero if one factor =0

so

x-1=0

or

x+5=0

solving, we get x=1 or x=-5

Answer 2

`x = 1\: or \: x = - 5`

EXPLANATION

The given rational expression is

`((x - 1)(x + 5))/(x - 5)`

For the given rational function to be zero, then the numerator must be equal to zero.

We now equate the numerator to zero and solve for x.

This implies that,

`(x - 1)(x + 5) = 0`

We use the zero product property to obtain,

`(x - 1) = 0 \: or \: (x + 5) = 0`

`x = 1\: or \: x = - 5`

Hence the zeros of the given rational function are x=-5,x=1