least common denominator (LCD)
The number that results from calculating the lowest common multiple of the denominators of those same fractions is called the lowest common denominator of two or more fractions.
For this case:
((x ^ 2-x-6) / (x ^ 2)) = ((x-6) / (2x)) + ((2x + 12) / (x))
LCD = x ^ 2
Multiplying both sides by LCD
x ^ 2 ((x ^ 2-x-6) / (x ^ 2)) = x ^ 2 (((x-6) / (2x)) + ((2x + 12) / (x)))
Simplifying
(x ^ 2-x-6) = ((x ^ 2-6x) / (2)) + (2x ^ 2 + 12x))
(2x ^ 2-2x-12) = ((x ^ 2-6x) + (4x ^ 2 + 24x))
(2x ^ 2-2x-12) = (5x ^ 2 + 18x)
3x ^ 2 + 20x + 12 = 0
the answer is
3x ^ 2 + 20x + 12 = 0
