Question

6.\(Q=\left(\frac{\sqrt{x}-4}{x-2\sqrt{x}}-\frac{3}{2-\sqrt{x}}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}\right)\)

Answer 1

\(Q=\left(\frac{\sqrt{x}-4}{x-2\sqrt{x}}-\frac{3}{2-\sqrt{x}}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}\right)\)

\(=\left(\frac{\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}+\frac{3}{\sqrt{x}-2}\right):\left(\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{x}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)

\(=\frac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}:\frac{x-4-x}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

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

\(=1-\sqrt{x}\)