\(\sqrt{2}\left(\sqrt{21}+3\right)\sqrt{5-\sqrt{21}}=\sqrt{3}\left(\sqrt{7}+\sqrt{3}\right)\sqrt{10-2\sqrt{21}}\)
\(=\sqrt{3}\left(\sqrt{7}+\sqrt{3}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\sqrt{3}\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{3}\left(7-3\right)=4\sqrt{3}\)
ĐKXĐ: \(x>0\)
\(\left(\frac{1}{\sqrt{x}+1}-\frac{1}{x+\sqrt{x}}\right):\frac{x-\sqrt{x}+1}{x\sqrt{x}+1}=\left[\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}-\frac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right].\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{x-\sqrt{x}+1}\)
\(\frac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}.\left(\sqrt{x}+1\right)=\frac{\sqrt{x}-1}{\sqrt{x}}\)