\(\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\frac{2+6\sqrt{3}}{\sqrt{3}}-\frac{13}{\sqrt{3}+4}\)

\(=\frac{\sqrt{3}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}+\frac{\sqrt{3}\left(\sqrt{3}+6\right)}{\sqrt{3}}-\frac{13\left(4-\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}\)

\(=-\sqrt{3}+\sqrt{3}+6-\frac{52-13\sqrt{3}}{16-3}\)

\(=6-\frac{52-13\sqrt{3}}{13}=\frac{78-52-13\sqrt{3}}{13}=\frac{26-13\sqrt{3}}{13}\)

\(=2-\sqrt{3}\)

ĐKXĐ: \(x\ge0;x\ne1;x\ne4\)

\(A=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{8\sqrt{x}}{x-1}\right):\frac{4\sqrt{x}-8}{1-x}\)

\(A=\left(\frac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{8\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\cdot\frac{1-x}{4\sqrt{x}-8}\)

\(A=\frac{x+2\sqrt{x}+1-x+2\sqrt{x}-1-8\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\frac{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}{4\sqrt{x}-8}\)

\(A=\frac{-4\sqrt{x}}{4\sqrt{x}-8}=\frac{\sqrt{x}}{2-\sqrt{x}}\)

1. \(A=\left(\frac{\sqrt{a}}{\sqrt{a}-2}+\frac{\sqrt{a}}{\sqrt{a}+2}\right):\frac{\sqrt{4a}}{a-4}\)

\(A=\left(\frac{\sqrt{a}\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}+\frac{\sqrt{a}\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right)\cdot\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{4a}}\)

\(A=\frac{a+2\sqrt{a}+a-2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{2\sqrt{a}}\)

\(A=\frac{2a}{2\sqrt{a}}=\sqrt{a}\)

ĐK : u, v > 0 , u khác v

\(=\frac{\left(\sqrt{u}-\sqrt{v}\right)\left(\sqrt{u}+\sqrt{v}\right)}{\sqrt{u}+\sqrt{v}}-\frac{\left(\sqrt{u}+\sqrt{v}\right)\left(u-\sqrt{uv}+v\right)}{\left(\sqrt{u}-\sqrt{v}\right)\left(\sqrt{u}+\sqrt{v}\right)}\)

\(=\sqrt{u}-\sqrt{v}-\frac{u-\sqrt{uv}+v}{\sqrt{u}-\sqrt{v}}\)

\(=\frac{u-2\sqrt{uv}+v-u+\sqrt{uv}-v}{\sqrt{u}-\sqrt{v}}=\frac{-\sqrt{uv}}{\sqrt{u}-\sqrt{v}}\)