Question

Rút gọn hộ mình biểu thức này với !!!!!!!!!!

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

Answer 1

ĐKXĐ : x > 0 ; x \(\ne\)4

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

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

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

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

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

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