Question

Answer 1

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

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

\(=\frac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-x+4}=\frac{4\sqrt{x}-4}{4}=\sqrt{x}-1\)

Thay \(x=3+\sqrt8=3+2\sqrt2=\left(\sqrt2+1\right)^2\) vào B, ta được:

\(B=\sqrt{\left(\sqrt2+1\right)^2}-1=\sqrt2+1-1=\sqrt2\)