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 } * \frac{x - 3}{ {x}^(2) + x - 12 }`

`\frac{x + 2}{ {x}^(2) + 2x - 5x - 10 } * \frac{x - 3}{ {x}^(2) + 4x - 3x - 12 }`

`(x + 2)/(x(x + 2) - 5(x + 2)) * (x - 3)/(x(x + 4) - 3(x + 4))`

`(x + 2)/((x + 2) * (x - 5)) * (x - 3)/((x + 4) * (x - 3))`

`(1)/((x + 4) * (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