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