$A=\frac{\sqrt{x}-1}{\sqrt{x}+1}B=\frac{\sqrt{x}+3}{\sqrt{x}-3}-\frac{4}{1-\sqrt{x}}+\frac{5-x}{x-1}\left(x\ge 0;x\ne 1\right)$ \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}$$ a)\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}$$ 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}$$ E=(\frac{3x-2}{x^2-9}-\frac{5x+1}{x^2-3x}-\frac{x+1}{x^2+3x}):\frac{x+2}{x^2+3x}-\frac{4^2-2x}{x^2-x-6}$A=\left(\frac{x+\sqrt{\mathrm{9x}}-1}{x+\sqrt{x}-2}-\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+2}\right):\frac{1}{x-1}\ge \ne \frac{1}{A}\sqrt{x+2\sqrt{x}+1}+\sqrt{x-2\sqrt{x}+1}=2\frac{\mathrm{1.3.5...}\left(2n-1\right)}{\mathrm{2.4.6...2}n}<\frac{1}{\sqrt{2n+1}}\forall n\in Z_{+}\frac{\mathrm{1.3.5...}\left(2n-1\right)}{\mathrm{2.4.6...2}n}<\frac{1}{\sqrt{2n+1}}\forall n\in Z_{+}\frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{3\sqrt{z}}{\sqrt{xz}+3\sqrt{z}+3}\sqrt{10P-1}\sqrt{xyz}\sqrt{x\left(4-y\right)\left(4-z\right)}+\sqrt{y\left(4-z\right)\left(4-x\right)}+\sqrt{z\left(4-x\left(4-y\right)\right)}\frac{x^2}{{\left(x+2\right)}^2}+3=3x^2-6x\{\begin{array}{c}{x}^2+y^2+xy+1=2x\\ x{\left(x+y\right)}^2+x-2=2y^2\end{array}{x}^2+x+2y^2+y=2x{y}^2+xy+3a_1^3+a_2^3+a_3^3+....+a_n^3{a}_1,a_2,a_3,...,a_n{2019}^{2018}{R}^2\sqrt{2}R\sqrt{2}\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=3\frac{a{b}^2}{a+b}+\frac{b{c}^2}{b+c}+\frac{c{a}^2}{c+a}a+b+c\le 1\frac{1}{a^2+2bc}+\frac{1}{b^2+2ac}+\frac{1}{c^2+2ab}\ge 9\left(\frac{1}{1-\sqrt{x}}+\frac{1}{1+\sqrt{x}}\right):\left(\frac{1}{1-\sqrt{x}}-\frac{1}{1+\sqrt{x}}\right)+\frac{1}{2\sqrt{x}}$ \Delta :y=kx-k+2$$ k$$ k$$