How to simplify sqrt(2)/(sqrt(2) - 1) to 2 + sqrt(2)

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To simplify sqrt(2)/(sqrt(2) - 1) to 2 + sqrt(2), multiply the numerator and denominator by the conjugate of the denominator, which is (sqrt(2) + 1). This process eliminates the radical in the denominator, resulting in a simplified expression. The final result is indeed 2 + sqrt(2). Understanding the use of conjugates is key in rationalizing expressions involving square roots. The discussion highlights a common challenge in algebraic simplification, emphasizing the importance of recognizing conjugates.
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Homework Statement


I feel really stupid asking this, but I'm working on infinite series and my answer is sqrt(2)/(sqrt(2)-1) The book simplifies this to 2 + sqrt(2) and I don't know how this simplification occurs. I'm sure the answer is really obvious and I sure feel stupid not seeing it! Any help is appreciated.

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The Attempt at a Solution

 
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nevermind, I see now that it was the conjugate... :)
 

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