Rút gọn biểu thức

Question

 Rút gọn P= 

Answer 1

Chúc bạn học tốt

_nguyendavit123_

Answer 2

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