Question

How do you simplify `(3x)/(x^2-x-6) + (x+2) / (x^2-6x+9)`?

Answer 1

`(4x^2-5x+4)/(x^3-4x^2-3x+18)`

Explanation:

Let's combine the fractions by first factoring the denominators:

`(3x)/(x^2-x-6)+(x+2)/(x^2-6x+9)`

`(3x)/((x-3)(x+2))+(x+2)/((x-3)(x-3))`

`(3x)/((x-3)(x+2))((x-3)/(x-3))+(x+2)/((x-3)(x-3))((x+2)/(x+2))`

`(3x^2-9x)/((x-3)(x-3)(x+2))+(x^2+4x+4)/((x-3)(x-3)(x+2))`

`(4x^2-5x+4)/((x-3)(x-3)(x+2))=(4x^2-5x+4)/(x^3-4x^2-3x+18)`