Question

\(A=\left(\frac{1}{\sqrt{x}-2}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}+1}\right)\)

Rut gon A

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Answer 1

\(A=\left(\frac{1}{\sqrt{x}-2}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-1}\right)\left(ĐK:x>0;x\ne1;x\ne4\right)\)

\(=\frac{\sqrt{x}-\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}-2\right)}:\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{2}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{x-1-x+4}\)

\(=\frac{2\left(\sqrt{x}+1\right)}{3\sqrt{x}}\)