a, ĐK: \(x\ge1;x\ne3\)
\(P=\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}\)
\(=\dfrac{\left(x-3\right)\left(\sqrt{x-1}+\sqrt{2}\right)}{x-1-2}\)
\(=\dfrac{\left(x-3\right)\left(\sqrt{x-1}+\sqrt{2}\right)}{x-3}\)
\(=\sqrt{x-1}+\sqrt{2}\)
a: \(P=\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}=\sqrt{x-1}+\sqrt{2}\)
b: \(P=\sqrt{8-4\sqrt{3}-1}+\sqrt{2}\)
\(=2-\sqrt{3}+\sqrt{2}\)
b, \(P=\sqrt{x-1}+\sqrt{2}\)
\(=\sqrt{4\left(2-\sqrt{3}\right)-1}+\sqrt{2}\)
\(=\sqrt{7-4\sqrt{3}}+\sqrt{2}\)
\(=\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{2}\)
\(=2-\sqrt{3}+\sqrt{2}\)
