SOLUTION: I am using the conjugate of my original equation, {{{sqrt(x^2+x)-x}}}, and trying to simplify it. please explain how to factor x out of the denominator of the following expression:

Algebra ->  Real-numbers -> SOLUTION: I am using the conjugate of my original equation, {{{sqrt(x^2+x)-x}}}, and trying to simplify it. please explain how to factor x out of the denominator of the following expression:      Log On


   

Question 391227: I am using the conjugate of my original equation, sqrt%28x%5E2%2Bx%29-x, and trying to simplify it. please explain how to factor x out of the denominator of the following expression: %28x%5E2%2Bx-x%5E2%29%2F%28sqrt%28x%5E2%2Bx%29%2Bx%29. My textbook states that x%2F%28sqrt%281%2B%281%2Fx%29%29%2B1%29 is supposed to be the answer, but I do not understand how to factor the radical. many, many thanks!
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2Bx-x%5E2%29%2F%28sqrt%28x%5E2%2Bx%29%2Bx%29
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Multiply NUM and DEN by the conjugate of the DEN, %28sqrt%28x%5E2%2Bx%29-x%29.
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Your NUM is %28x%5E2%2Bx-x%5E2%29 = x ???
You mention an "original equation", but don't show it ???

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + x = x^2 + (x^2 / x)

factoring ___ x^2[1 + (1/x)]

sqrt{x^2[1 + (1/x)]} + x = x {sqrt[1 + (1/x)] + 1}