Question

what is the simplified form of x+2/x^2-3x-10 * x-3/x^2+x-12
1/(x-3)(x+4)
1/(x-3)(x+2)
1/(x+4)(x-5)
1/(x+2)(x-5)

Answer 1

i mean based on your possible answers, the third one is correct,but you can go further that that, in the steps i will note when you've came to the "answer"

$\frac{x + 2}{ {x}^{2} - 3x - 10 } \times \frac{x - 3}{ {x}^{2} + x - 12 }$
$\frac{x + 2}{ {x}^{2} + 2x - 5x - 10 } \times \frac{x - 3}{ {x}^{2} + 4x - 3x - 12 }$
$\frac{x + 2}{x(x + 2) - 5(x + 2)} \times \frac{x - 3}{x(x + 4) - 3(x + 4)}$
$\frac{x + 2}{(x + 2) \times (x - 5)} \times \frac{x - 3}{(x + 4) \times (x - 3)}$
$\frac{1}{(x + 4) \times (x + 5)}$
and basically that's the "answer", but you can simplify more.

$\frac{1}{ {x}^{2} + 4x - 5x - 20}$
$\frac{1}{ {x}^{2} - x - 20 }$
Hope that's helpful