Question

Tính P = \(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt[]{x}}{4-x}\)

Answer 1

\(P=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)

\(P=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)}{x-4}+\frac{2\sqrt{x}\left(\sqrt{x}-2\right)}{x-4}+\frac{-5\sqrt{x}-2}{x-4}\)

\(P=\frac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{x-4}\)

\(P=\frac{3x-6\sqrt{x}}{x-4}\)

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

\(P=\frac{3\sqrt{x}}{\sqrt{x}+2}\)