Question

A = (sqrt(x))/(sqrt(x) - 1) + 1/(sqrt(x) + 2) - (3sqrt(x))/(x + sqrt(x) - 2)

Answer 1

Answer 2

\(A=\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+2}-\dfrac{3\sqrt{x}}{x+\sqrt{x}-2}\left(x\ge0\right)\\ A=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)+\left(\sqrt{x}-1\right)-3\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\\ A=\dfrac{x+2\sqrt{x}+\sqrt{x}-1-3\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\\ A=\dfrac{x-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)

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