5x + 7/x^2-2x-8 - 2x+19/x^2x-8

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)