\(2\sqrt{a}-a\sqrt{\dfrac{4}{a}}\)

\(=2\sqrt{a}-a.\dfrac{\sqrt{4}}{\sqrt{a}}\)

\(=2\sqrt{a}-a.\dfrac{2}{\sqrt{a}}\)

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

\(=0\)

\(B=\frac{3\sqrt{x}+1}{x+2\sqrt{x}-3}-\frac{2}{\sqrt{x}+3}\) ĐK : \(x\ge0;x\ne1\)

\(=\frac{3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{2}{\sqrt{x}+3}\)

\(=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{1}{\sqrt{x}-1}\)

\(=\frac{3\sqrt{x}+1}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}-\frac{2}{\sqrt{x}+3}\)   

\(=\frac{3\sqrt{x}+1-2\cdot\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)   

\(=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)   

\(=\frac{\sqrt{x}+3}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)   

\(=\frac{1}{\sqrt{x}-1}\)

\(B=\frac{3\sqrt{x}+1}{x+2\sqrt{x}-3}-\frac{2}{\sqrt{x}+3}\)

\(=\frac{3\sqrt{x}+1-2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)

\(=\frac{\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{1}{\sqrt{x}-1}\)

a: \(\sqrt{\frac47}-10\sqrt{\frac{7}{25}}-6\cdot\sqrt{\frac{1}{28}}\)

\(=\frac{2}{\sqrt7}-10\cdot\frac{\sqrt7}{5}-6\cdot\frac{1}{2\sqrt7}\)

\(=\frac27\sqrt7-2\sqrt7-\frac{3\sqrt7}{7}=-\frac{15}{7}\sqrt7\)

b: \(\left(\sqrt{10}+\sqrt2\right)\cdot\sqrt{3-\sqrt5}\)

\(=\left(\sqrt5+1\right)\cdot\sqrt{6-2\sqrt5}\)

\(=\left(\sqrt5+1\right)\cdot\sqrt{\left(\sqrt5-1\right)^2}=\left(\sqrt5+1\right)\left(\sqrt5-1\right)\)

=5-1

=4

c: \(\frac{\sqrt{6+\sqrt{11}}-\sqrt{7-\sqrt{33}}}{\sqrt6+\sqrt2}\)

\(=\frac{\sqrt{12+2\sqrt{11}}-\sqrt{14-2\sqrt{33}}}{2\left(\sqrt3+1\right)}\)

\(=\frac{\sqrt{\left(\sqrt{11}+1\right)^2}-\sqrt{\left(\sqrt{11}-\sqrt3\right)^2}}{2\left(\sqrt3+1\right)}=\frac{\sqrt{11}+1-\sqrt{11}+\sqrt3}{2\left(1+\sqrt3\right)}\)

\(=\frac{1+\sqrt3}{2\left(1+\sqrt3\right)}=\frac12\)

d: \(\frac{5\sqrt3-3\sqrt5}{\sqrt5-\sqrt3}+\frac{2}{4+\sqrt{15}}-\frac{5\sqrt5+3\sqrt3}{\sqrt5+\sqrt3}\)

\(=\frac{\sqrt{15}\left(\sqrt5-\sqrt3\right)}{\sqrt5-\sqrt3}+\frac{2\left(4-\sqrt{15}\right)}{\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right)}-\frac{\left(\sqrt5+\sqrt3\right)\left(8-\sqrt{15}\right)}{\sqrt5+\sqrt3}\)

\(=\sqrt{15}+2\left(4-\sqrt{15}\right)-\left(8-\sqrt{15}\right)\)

\(=2\sqrt{15}-8+8-2\sqrt{15}\)

=0

a: \(=\dfrac{x-\sqrt{x}-x-2\sqrt{x}-1-2\sqrt{x}-4}{x-1}\)

\(=\dfrac{-5\sqrt{x}-5}{x-1}=\dfrac{-5}{\sqrt{x}-1}\)

b: \(=\dfrac{5x+10\sqrt{x}+\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)-6x}{x-4}\)

\(=\dfrac{-x+10\sqrt{x}+x-5\sqrt{x}+6}{x-4}\)

\(=\dfrac{5\sqrt{x}+6}{x-4}\)

Với \(x\ge0;x\ne\pm16\)

\(B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\)

\(=\left(\frac{x-4\sqrt{x}+4\sqrt{x}+16}{x-16}\right):\frac{x+16}{\sqrt{x}-2}=\frac{\sqrt{x}-2}{x-16}\)

\(\left(\sqrt{75}+\sqrt{243}-\sqrt{48}\right):\sqrt{3}\)

\(=\sqrt{75}:\sqrt{3}+\sqrt{243}:\sqrt{3}-\sqrt{48}:\sqrt{3}\)

\(=\sqrt{75:3}+\sqrt{243:3}-\sqrt{48:3}\)

\(=\sqrt{25}+\sqrt{81}-\sqrt{16}\)

\(=5+9-4=10\)