Question

[chi mai Nguyen]

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

Rút gọn P

Answer 1

[Edogawa Conan]

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

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

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

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

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