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

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)