Question

$\sqrt{x + 2 \sqrt{x - 1} } - \sqrt{x - 2 \sqrt{x - 1} }$
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Answer 1

$\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1+2\sqrt{x-1}+1}-\\ \\ \\ -\sqrt{x-1-2\sqrt{x-1}+1}=\sqrt{(\sqrt{x-1}+1)^2}-\sqrt{(\sqrt{x-1}-1)^2}=\\ \\ \\ =|\sqrt{x-1}+1|-|\sqrt{x-1}-1|$