Rút gọn biểu thức :
P = $\frac{2\sqrt{x}}{x-1}$ – $\frac{1}{1-\sqrt{x} }$ + $\frac{\sqrt{x}}{\sqrt{x}+1}$ ( x ≥ 0 , x $\neq$ 1)
Rút gọn biểu thức :
P = $\frac{2\sqrt{x}}{x-1}$ – $\frac{1}{1-\sqrt{x} }$ + $\frac{\sqrt{x}}{\sqrt{x}+1}$ ( x ≥ 0 , x $\neq$ 1)
Đáp án:
$P = \dfrac{\sqrt x +1}{\sqrt x – 1}$
Giải thích các bước giải:
$\begin{array}{l}P = \dfrac{2\sqrt x}{x – 1} -\dfrac{1}{1-\sqrt x} +\dfrac{\sqrt x}{\sqrt x + 1}\qquad (x \geq 0;\, x \ne 1)\\ \to P =\dfrac{2\sqrt x}{(\sqrt x -1)(\sqrt x+1)} + \dfrac{\sqrt x+1}{(\sqrt x -1)(\sqrt x+1)} + \dfrac{\sqrt x(\sqrt x -1)}{(\sqrt x -1)(\sqrt x+1)}\\ \to P = \dfrac{2\sqrt x + \sqrt x + 1 +x – \sqrt x}{(\sqrt x -1)(\sqrt x+1)}\\ \to P = \dfrac{ x + 2\sqrt x+1}{(\sqrt x -1)(\sqrt x+1)}\\ \to P = \dfrac{(\sqrt x + 1)^2}{(\sqrt x -1)(\sqrt x+1)}\\ \to P = \dfrac{\sqrt x+1}{\sqrt x – 1}\end{array}$