Question

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

Answer 1

Given:

The expression is

$\dfrac{x-5}{3x^2-10x-25}$

To find:

The restricted value of given expression.

Solution:

We have,

$\dfrac{x-5}{3x^2-10x-25}$

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

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

$x=5\text{ and }x=-\dfrac{5}{3}$

Therefore, the restricted values are $x=5\text{ and }x=-\dfrac{5}{3}$.