Simplify 10-x^2-3x/x^2+2x-8
identify any x-values for which the expression is undefined.

10-x^2-3x=0 implies x=2 and x=-5, so 10-x^2-3x= (x-2)(x+5)
x^2+2x-8=0 implies x= -4 and x=2, so x^2+2x-8 =(x+4)(x-2)
10-x^2-3x/x^2+2x-8 = (x-2)(x+5) / (x+4)(x-2) = (x+5) / (x+4)

the expression is undefined if x+4 =0, it means x= - 4