SOLUTION: 4/x-3 + 2x\xsquared-9 = 1/x+3

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Question 1026531: 4/x-3 + 2x\xsquared-9 = 1/x+3
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!

multiply equation by

4(x+3)+2x = (x-3)

4x+12+2x =x-3
5x=-15
x=-3

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
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        This problem is very tricky.
        It contains a hidden trap that's easy to fall into.
        Tutor @mananth didn't avoid this trap — he fell into it and produced an incorrect solution,
        for which he deserves a solid F.

        Below is my correct solution to replace @mananth's incorrect one.

Your starting equation is + = . Notice that the domain of this equation is the set of all real numbers except of x = 3 and/or x = -3, where the denominators are not defined. So, we will work on the domain x =/= -3 and x =/= 3. Multiply both sides by (x^2-3). You will get 4(x+3) + 2x = x - 3, 4x + 12 + 2x = x - 3, 6x - x = -3 - 12 5x = -15, x = -15/5 = -3. But x = -3 is not in the domain. So, we conclude that the given equation HAS NO solutions in its domain. <<<---=== ANSWER

Solved correctly.

Answer by n2(78)   (Show Source):
You can put this solution on YOUR website!
.
4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
~~~~~~~~~~~~~~~~~~~~~~~~~

Your starting equation is + = . Notice that the domain of this equation is the set of all real numbers except of x = 3 and/or x = -3, where the denominators are not defined. So, we will work on the domain x =/= -3 and x =/= 3. Multiply both sides by (x^2-3). You will get 4(x+3) + 2x = x - 3, 4x + 12 + 2x = x - 3, 6x - x = -3 - 12 5x = -15, x = -15/5 = -3. But x = -3 is not in the domain. So, we conclude that the given equation HAS NO solutions in its domain. <<<---=== ANSWER

Solved.