Question

P = (x * sqrt(2))/(2sqrt(x) + x * sqrt(2)) + (sqrt(2x) - 2)/(x - 2)

Giúp em với ạ.

Answer 1

\(P=\dfrac{x\sqrt{2}}{2\sqrt{x}+x\sqrt{2}}+\dfrac{\sqrt{2x}-2}{x-2}\)

\(=\dfrac{x\sqrt{2}}{\sqrt{2x}\left(\sqrt{x}+\sqrt{2}\right)}+\dfrac{\sqrt{2}\left(\sqrt{x}-\sqrt{2}\right)}{x-2}\)

\(=\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{2}}+\dfrac{\sqrt{2}}{\sqrt{x}+\sqrt{2}}=1\)