After multiplying each side of the equation by the lcd and simplify , the resulting equation is

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

The volume is 56.8 triangular the