$\frac{\mathrm{\backslash (\backslash dfrac\{2\backslash sqrt\{x\}\}\{\backslash sqrt\{x+\}3\}+\backslash dfrac\{\backslash sqrt\{x\}+1\}\{\backslash sqrt\{x\}-3\}+\backslash dfrac\{3-11\backslash sqrt\{x\}\}\{9-x\},x\backslash ge0,x\backslash ne9\backslash )}}{}$ 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}$A=\left(\frac{x+\sqrt{\mathrm{9x}}-1}{x+\sqrt{x}-2}-\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+2}\right):\frac{1}{x-1}\ge \ne \frac{1}{A}$ \frac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}$$ \frac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}$$ \frac{x+y+2xy}{1-xy}$$ \frac{2}{2+\sqrt{3}}$$ \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}$$ \frac{1}{4}$$ A=\frac{2x-\sqrt{x}+8}{2\sqrt{x}-1}$\left(\frac{1}{1-\sqrt{x}}+\frac{1}{1+\sqrt{x}}\right):\left(\frac{1}{1-\sqrt{x}}-\frac{1}{1+\sqrt{x}}\right)+\frac{1}{2\sqrt{x}}\sqrt{\frac{1}{9}.0,64.64}\sqrt{11\frac{1}{9}}\sqrt{\frac{1}{144}}.2\frac{2}{49}\sqrt{1\frac{9}{16}}.2\frac{1}{4}.2\frac{7}{9}$ \sqrt{\frac{9}{{\left(x-2\right)}^2}}$$ \sqrt{\frac{a}{6}}$$ \sqrt{\frac{2a}{3}}$$ \sqrt{\frac{3a}{2}}$$ \sqrt{9a^2}$$ \sqrt{4a^2}$$ \sqrt{{\left(1-a\right)}^2}$$ \sqrt{16a^2}$$ \left|x-2\right|$$ \frac{\sqrt{x^2}}{x}$$ \frac{x^2+2\sqrt{3}.x+3}{x^2-3}$$ \left|x-\sqrt{{\left(x-1\right)}^2}\right|$$ -$$ \frac{2\sqrt{x}}{x+1}$$ \sqrt{p}$$ \sqrt{3x-1}-\sqrt{x+1}=3x^2-2x-1$$ (x+1)\sqrt{x^2-5x+3}=x^2+1$$ x^2+4x+5=2\sqrt{2x+3}$$