$\frac{1}{\sqrt{1}+\surd \sqrt{2}}+\frac{1}{\sqrt{2}+\surd \sqrt{3}}+\frac{1}{\sqrt{3}+\surd \sqrt{4}}+...+\frac{1}{\sqrt{99}+\surd \sqrt{100}}$ a)\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}$$ b)\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}$$ c)\sqrt{9-2\sqrt{14}}-\sqrt{9-2\sqrt{14}}$$ d)\sqrt{2(4-\sqrt{7})}$$ e)\sqrt{a+1+2\sqrt{a}}$$ f)-\sqrt{2(2-\sqrt{3})}+\sqrt{2(2+\sqrt{3})}$$ g)\sqrt{x+y-2\sqrt{xy}}$$ (x\ge y)$$ h)\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$$ i)\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}$$ j)\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5-2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}-\sqrt{7+2\sqrt{10}}}}$$ k)\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}$$ l)\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}$$ m\left)\right(4+\sqrt{15}\left)\right(\sqrt{10}-\sqrt{6}\left)\right(4-\sqrt{15})$$ n\left)\sqrt{3-\sqrt{5}}\right(\sqrt{10}-\sqrt{2}\left)\right(3+\sqrt{5})$$ o)\sqrt{31+2}.\sqrt{6+\sqrt{5+\sqrt{2}}}.+\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}$$ a)x-\sqrt{x}$$ b)x-1$$ c)x-2\sqrt{2}+1$$ d)-x+3\sqrt{x}+4$$ e)2x-\sqrt{x}-1$$ f)x-\sqrt{2}-2$$ g)x\sqrt{x}+1$$ h)2x+\sqrt{x}-3$$ i)x\sqrt{x}+9x+14\sqrt{x}$$ j)2x\sqrt{x}+5x+3\sqrt{x}$$ E=(\frac{3x-2}{x^2-9}-\frac{5x+1}{x^2-3x}-\frac{x+1}{x^2+3x}):\frac{x+2}{x^2+3x}-\frac{4^2-2x}{x^2-x-6}$$ \left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$ \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{2\sqrt{x}}{x+1}$$ \sqrt{p}$$ \sqrt{3x-1}-\sqrt{x+1}=3x^2-2x-1$$ (x+1)\sqrt{x^2-5x+3}=x^2+1$$ x^2+4x+5=2\sqrt{2x+3}$$ \left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$ \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{}{}$$ \frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{3\sqrt{z}}{\sqrt{xz}+3\sqrt{z}+3}$$ \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}$A=\left(\frac{x+\sqrt{\mathrm{9x}}-1}{x+\sqrt{x}-2}-\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+2}\right):\frac{1}{x-1}\ge \ne \frac{1}{A}$ \$\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}$\left(\frac{1}{1-\sqrt{x}}+\frac{1}{1+\sqrt{x}}\right):\left(\frac{1}{1-\sqrt{x}}-\frac{1}{1+\sqrt{x}}\right)+\frac{1}{2\sqrt{x}}$