SOLUTION: Solve the rational equation: x/(x+2) - 3/(x-2) = (2x+12)/(x^2-4)

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Question 62197: Solve the rational equation: x/(x+2) - 3/(x-2) = (2x+12)/(x^2-4)
Answer by uma(370) About Me  (Show Source):
You can put this solution on YOUR website!
x/(x+2) - 3/(x-2) = (2x+12)/(x^2-4)
We know (x+2)(x-2) = (x^2-4)
Multiplying through out by the LCD = (x+2)(x-2)...
x(x-2) - 3(x+2) = 2x+12
==> x^2 - 2x - 3x - 6 = 2x + 12
==> x^2 - 5x - 6 = 2x + 12
==> x^2 - 5x - 6 - 2x - 12 = 0 [adding - 2x - 12 to both the sides]
==> x^2 - 7x - 18 = 0
==> x^2 - 9x + 2x - 18 = 0 [splitting the middle term]
==> x(x-9) + 2(x-9) = 0 [removing the common factor]
==> (x-9)(x+2) = 0
==> x-9 = 0 or x+2 = 0
==> x = 9 or x = -2
Good Luck!!!