Question

A=\(y=\frac{x\sqrt{x}}{x-1}\)-\(-\frac{x-1}{\sqrt{x}+1}\)

Answer 1

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Answer 2

\(A=\frac{\sqrt{x}^3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}+1}\)

\(=\frac{x\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\left(\sqrt{x}-1\right)=\frac{x\sqrt{x}-\left(\sqrt{x}-1\right)\left(x-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

\(=\frac{x\sqrt{x}-x\sqrt{x}+\sqrt{x}+x-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\frac{x+\sqrt{x}-1}{x-1}\)