Given:
The expression is
[tex]\dfrac{x-5}{3x^2-10x-25}[/tex]
To find:
The restricted value of given expression.
Solution:
We have,
[tex]\dfrac{x-5}{3x^2-10x-25}[/tex]
Equate the denominate equal to 0, to find the restricted value.
[tex]3x^2-10x-25=0[/tex]
[tex]3x^2-15x+5x-25=0[/tex]
[tex]3x(x-5)+5(x-5)=0[/tex]
[tex](x-5)(3x+5)=0[/tex]
Using zero product property, we get
[tex]x-5=0\text{ and }3x+5=0[/tex]
[tex]x=5\text{ and }x=-\dfrac{5}{3}[/tex]
Therefore, the restricted values are [tex]x=5\text{ and }x=-\dfrac{5}{3}[/tex].
