Lời giải:
\(M=\frac{\sqrt{x-2\sqrt{2}}}{\sqrt{x^2-4x\sqrt{2}+8}}-\frac{\sqrt{x+2\sqrt{2}}}{\sqrt{x^2+4x\sqrt{2}+8}}\)
\(=\frac{\sqrt{x-2\sqrt{2}}}{\sqrt{(x-2\sqrt{2})^2}}-\frac{\sqrt{x+2\sqrt{2}}}{\sqrt{(x+2\sqrt{2})^2}}=\frac{\sqrt{x-2\sqrt{2}}}{x-2\sqrt{2}}-\frac{\sqrt{x+2\sqrt{2}}}{x+2\sqrt{2}}\)
\(=\frac{1}{\sqrt{x-2\sqrt{2}}}-\frac{1}{\sqrt{x+2\sqrt{2}}}\)
Thay $x=3$:
\(M=\frac{1}{\sqrt{3-2\sqrt{2}}}-\frac{1}{\sqrt{3+2\sqrt{2}}}=\frac{1}{\sqrt{2-2\sqrt{2}+1}}-\frac{1}{\sqrt{2+2\sqrt{2}+1}}\)
\(=\frac{1}{\sqrt{(\sqrt{2}-1)^2}}-\frac{1}{\sqrt{(\sqrt{2}+1)^2}}=\frac{1}{\sqrt{2}-1}-\frac{1}{\sqrt{2}+1}=\frac{2}{(\sqrt{2}-1)(\sqrt{2}+1)}=\frac{2}{2-1}=2\)
