Bài 4:
\(P=\frac{x\sqrt{2}}{\sqrt{2x}(\sqrt{2}+\sqrt{x})}+\frac{\sqrt{2}(\sqrt{x}-\sqrt{2})}{(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})}\)
\(=\frac{\sqrt{x}}{\sqrt{2}+\sqrt{x}}+\frac{\sqrt{2}}{\sqrt{x}+\sqrt{2}}=\frac{\sqrt{x}+\sqrt{2}}{\sqrt{x}+\sqrt{2}}=1\)
Bài 5:
\(Q=\left[\frac{a}{\sqrt{a}(\sqrt{a}-2)}+\frac{a}{\sqrt{a}-2}\right]: \frac{\sqrt{a}+1}{(\sqrt{a}-2)^2}\)
\(=\left[\frac{\sqrt{a}}{\sqrt{a}-2}+\frac{a}{\sqrt{a}-2}\right].\frac{(\sqrt{a}-2)^2}{\sqrt{a}+1}=\frac{\sqrt{a}+a}{\sqrt{a}-2}.\frac{(\sqrt{a}-2)^2}{\sqrt{a}+1}\)
\(=\frac{\sqrt{a}(1+\sqrt{a})(\sqrt{a}-2)^2}{(\sqrt{a}-2)(\sqrt{a}+1)}=\sqrt{a}(\sqrt{a}-2)\)