Solve:

x^2-x-6/x^2=x-6/2x+2x+12/x

After multiplying each side by the equation LCD and simplifying, the resulting equation is ...

First we look at the equation an determine our common denominator.

(X²-X-6) / X² = (X-6) / 2X + (2X+12) / X (let's use 2X² as the comm denom)

multiply the first fraction by 2, the second by X, and the third by 2x

(2x²-2x-12) / 2x² = (x²-6x) / 2x² + (4x²+24x) / 2x² (dropping the denominator)

2x² - 2x - 12 = x² - 6x + 4x² + 24x (simplify)

-3x² - 20x - 12 (multiply by - 1)

3x² + 20x + 12

(x + 6) (3x + 2) (factored version)