SOLUTION: x/(x+2) + 2/(x-2) = (-2x+19)/(x^2-4), solve for x (coukd be more than 1 answer)

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Question 62144: x/(x+2) + 2/(x-2) = (-2x+19)/(x^2-4), solve for x (coukd be more than 1 answer)
Answer by 303795(562) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%2B2%29+%2B+2%2F%28x-2%29+=+%28-2x%2B19%29%2F%28x%5E2-4%29 Factorise the expression on the bottom on the right as it is a difference of squares.
x%2F%28x%2B2%29+%2B+2%2F%28x-2%29+=+%28-2x%2B19%29%2F%28%28x-2%29%28x%2B2%29%29 Rewrite the problem over the LCD of (x-2)(x+2)
x%28x-2%29%2F%28%28x-2%29%28x%2B2%29%29+%2B+2%28x%2B2%29%2F%28%28x-2%29%28x%2B2%29%29+=+%28-2x%2B19%29%2F%28%28x-2%29%28x%2B2%29%29 Multiply both sides by the LCD of (x-2)(x+2) to eliminate the fraction part on the bottom.
x%28x-2%29+%2B+2%28x%2B2%29+=+-2x%2B19 Multiply out the terms on the left hand side.
x%5E2-2x+%2B+2x%2B4+=+-2x%2B19
x%5E2-2x+%2B+2x%2B4+=+-2x%2B19 Get all terms on one side of the equation
x%5E2%2B+2x-15+=+0 Factorise
%28x%2B5%29%28x-3%29+=+0
So the solutions are x=-5 or x=3