Question

what is the simplified form of x-5/x^2-3x-10*x+2/x^2+x-12

Answer 1

I assume you mean this, even though what you wrote means something else because you did not use parentheses.

$\dfrac{x-5}{x^2 - 3x - 10} \times \dfrac{x + 2}{x^2 + x - 12} =$

Factor each factorable polynomial.

$=\dfrac{x-5}{(x - 5)(x + 2)} \times \dfrac{x + 2}{(x + 4)(x - 3)}$

Now divide the numerator and denominator by the equal terms to reduce the fraction. This is what is normally called canceling factors.

$=\dfrac{1}{1} \times \dfrac{1}{(x + 4)(x - 3)}$

$=\dfrac{1}{(x + 4)(x - 3)}$

Answer 2

Collect like terms
(X-3x-10x+x) + (-5/x^2+2/x^2)-12

Then simplify
-11x-3/x^2-12

Let me know if that helped thanks