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Question 1140879: If I am to solve for x on this particular rational expression, then what would be the solution?
Here is the following expression: https://i.imgur.com/CNjknsR.png
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! from what i can tell, there is no solution to this problem.
x can't be + 2 and x can't be -2 because that would make the denominator equal to 0.
x^2 - 4 is equal to (x + 2) * (x - 2), so x = + 2 and x = - 2 is not allowed on either side of the equation.
the solution, if any, has to be something other than x = + 2 or x = - 2.
i solved in the following manner.
start with x / (x + 2) - x / (x - 2) = (x^2 + 4) / (x^2 - 4)
since (x^2 - 4) = (x + 2) * (x - 2), the equation becomes:
x / (x + 2) - x / (x - 2) = (x^2 + 4) / ((X - 2) * (X + 2))
multiply both sides of the equation by (x - 2) * (x + 2) to get:
x * (x - 2) - x * (x + 2) = x^2 + 4
simplify to get x^2 - 2x - x^2 - 2x = x^2 + 4
combine like terms to get -4x = x^2 + 4
add 4x to both sides of the eqution to get 0 = x^2 + 4x + 4
factor to get 0 = (x + 2) * (x + 2)
solve for x to get x = -2.
but x = -2 is not allowed because that would make the denominator in the original equation undefined.
therefore, there is no solution to the problem as far as i can see.
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