Cho biểu thức A=$\left(\frac{\sqrt{x}+2}{\sqrt{x}+1}-\frac{2\sqrt{x}-2}{\sqrt{x}-1}\right)\left(x-1\right)x\ge 0;x\ne 1$ \left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$ \left(1-\frac{2-\sqrt{2}}{1-\sqrt{2}}\right)$$ \frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}$$ \frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}$$ \frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}$$ \left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)$$ \frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}$$ \$\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-4\sqrt{\frac{3}{2}}=\frac{\sqrt{6}}{6}$$ \left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right):\sqrt{6x}=2\frac{1}{3}$$ P=\frac{\sqrt{x}-2}{\sqrt{x}-3}+\frac{\sqrt{x}+1}{\sqrt{x}+3}+\frac{x-4\sqrt{x}-9}{9-x}$$ Q=\frac{\sqrt{x}+5}{3-\sqrt{x}}$$ x\ge 0;x\ne 9$$ M=P:Q$$ \left|M\right|<\frac{1}{2}$$ a,b,c,d>0$$ \frac{a-d}{b+d}+\frac{d-b}{b+c}+\frac{b-c}{c+a}+\frac{c-a}{a+d}\ge 0$$ \frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{3\sqrt{z}}{\sqrt{xz}+3\sqrt{z}+3}$$ \sqrt{10P-1}$$ \frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{3\sqrt{z}}{\sqrt{xz}+3\sqrt{z}+3}$$ \sqrt{10P-1}$$ \left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$ \left(1-\frac{2-\sqrt{2}}{1-\sqrt{2}}\right)$$ \frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}$$ \frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}$$ \frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}$$ \left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)$$ \frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}$$ \frac{}{}$$ \frac{\sqrt{x}+4}{\sqrt{x}-1}$$ \frac{3\sqrt{x}+1}{x+2\sqrt{x}-3}-\frac{2}{\sqrt{x}+3}\left(x\ge 0,x\ne 1\right)$$ \frac{A}{B}\ge \frac{x}{4}+5$$ \frac{1}{\sqrt{x}-1}$$ \frac{4\left(\sqrt{x}+1\right)}{25-x}$$ \left(\frac{15-5x}{x-25}+\frac{2}{\sqrt{x}+5}\right):\frac{\sqrt{x}+1}{\sqrt{x}-5}\left(x\ge 0,x\ne 25\right)$$ \le $$ \frac{a}{b+c-a}+\frac{b}{c+a-b}+\frac{c}{a+b-c}\ge 3\left(2\right)$$ \frac{a^2}{b+c-1}+\frac{b^2}{c+a-b}+\frac{c^2}{a+b-c}\ge a+b+c\left(3\right)$$ \frac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}$$ \frac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}$$ \frac{x+y+2xy}{1-xy}$$ \frac{2}{2+\sqrt{3}}$$