Answer:
1 and -5
Step-by-step 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
[tex]x = 1\: or \: x = - 5[/tex]
EXPLANATION
The given rational expression is
[tex] \frac{(x - 1)(x + 5)}{x - 5} [/tex]
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,
[tex](x - 1)(x + 5) = 0[/tex]
We use the zero product property to obtain,
[tex](x - 1) = 0 \: or \: (x + 5) = 0[/tex]
[tex]x = 1\: or \: x = - 5[/tex]
Hence the zeros of the given rational function are x=-5,x=1
