Question

Which of the following is the restricted value of (x-5)/(〖3x〗^2-10x-25) ? *

Answer 1

Given:

The expression is

`(x-5)/(3x^2-10x-25)`

To find:

The restricted value of given expression.

Solution:

We have,

`(x-5)/(3x^2-10x-25)`

Equate the denominate equal to 0, to find the restricted value.

`3x^2-10x-25=0`

`3x^2-15x+5x-25=0`

`3x(x-5)+5(x-5)=0`

`(x-5)(3x+5)=0`

Using zero product property, we get

`x-5=0\text{ and }3x+5=0`

`x=5\text{ and }x=-(5)/(3)`

Therefore, the restricted values are
`x=5\text{ and }x=-(5)/(3)`.