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"
[tex] \frac{x + 2}{ {x}^{2} - 3x - 10 } \times \frac{x - 3}{ {x}^{2} + x - 12 } [/tex]
[tex] \frac{x + 2}{ {x}^{2} + 2x - 5x - 10 } \times \frac{x - 3}{ {x}^{2} + 4x - 3x - 12 } [/tex]
[tex] \frac{x + 2}{x(x + 2) - 5(x + 2)} \times \frac{x - 3}{x(x + 4) - 3(x + 4)} [/tex]
[tex] \frac{x + 2}{(x + 2) \times (x - 5)} \times \frac{x - 3}{(x + 4) \times (x - 3)} [/tex]
[tex] \frac{1}{(x + 4) \times (x + 5)} [/tex]
and basically that's the "answer", but you can simplify more.
[tex] \frac{1}{ {x}^{2} + 4x - 5x - 20} [/tex]
[tex] \frac{1}{ {x}^{2} - x - 20 } [/tex]
Hope that's helpful
