Since they have the same denominator, you just subtract the numerators:
= (5x + 7 - 2x - 19)/(x^2 - 2x - 8)
= (3x - 12)/(x^2 - 2x - 8)
To solve the first factor, you factorize by taking what's common
The common between 3x and 12 is 3
So it becomes 3(x - 4) dividing 3x and 12 each by 3
To factorize the quadratic equation x^2 - 2x - 8, you have to find two numbers if you add them they give you b which is -2, and if you multiply them they give you c which is -8
You get the two numbers -4 and 2
So the factorization of the quadratic equation is (x - 4)(x + 2) which is generally in the form of (x + s1)(x + s2)
So you get:
3(x - 4)/(x - 4)(x + 2)
You divide the numerator and the denominator by the factor (x - 4)
So you get as a final answer:
3/(x + 2)