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Algebra/Cross multiply with lcd

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Expert: - 2/11/2011


Question
X+1/x+6 + 1/x = 2x+1/x+6

Answer
The equatioin looks like it should be (x+1)/(x+6) + 1/x = (2x+1)/(x+6).
This said, multiply the entire equation by [(x+6)x]

That would gives x(x+1) + x+6 = x(2x+1).
That is x^2 + x + x + 6 = 2x^2 + x.

Combing like terms gives  x^2 + 2x + 6 = 2x^2 + x.
Subtracting the lefts side from both sides gives 0 = x^2 - x - 6.
Factoring gives 0 = (x-3)(x+2).

The solution would be x = 3 or x = -2.  

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