Answer:
To find the restricted values of x for the given rational expression,
[tex]\frac{x^2+8}{x^2-x-12}[/tex]The above expression is defined only when x^2-x-12 not equal to 0.
x values are restricted for the solution of x^2-x-12=0
To find the values of x when x^2-x-12=0.
Consider, x^2-x-12=0
we get,
[tex]x^2-x-12=0[/tex][tex]x^2-4x+3x-12=0[/tex][tex]x\left(x-4\right)+3\left(x-4\right)=0[/tex]Taking x-4 as common we get,
[tex]\left(x-4\right)\left(x+3\right)=0[/tex]we get, x=4,x=-3
The restricted values of x are 4,-3.
we get,
[tex]x\ne4,-3[/tex]Answer is:
[tex]x\ne4,-3[/tex]