$ P=\dfrac{ \left( \dfrac{ √x-1 }{ 3√x-1 } - \dfrac{ 1 }{ 3√x+1 } + \dfrac{ 8√x }{ 9x-1 } \right) }{ \left( 1- \dfrac{ 3√x-2 }{ 3√x+1 } \right) } $ a, Rút gọn P b,Tìm các giá trị x để P=6/5

Đáp án + Giải thích các bước giải:

 a) $P = \dfrac{\bigg(\dfrac{\sqrt{x} - 1}{3\sqrt{x} - 1} - \dfrac{1}{3\sqrt{x} + 1} + \dfrac{8\sqrt{x}}{9x - 1}\bigg)}{1 - \dfrac{3\sqrt{x} - 2}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{\sqrt{x} - 1}{3\sqrt{x} - 1} - \dfrac{1}{3\sqrt{x} + 1} + \dfrac{8\sqrt{x}}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3\sqrt{x} + 1}{3\sqrt{x} + 1} - \dfrac{3\sqrt{x} - 2}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{(\sqrt{x} - 1)(3\sqrt{x} + 1)}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} - \dfrac{3\sqrt{x} - 1}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} + \dfrac{8\sqrt{x}}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3\sqrt{x} + 1 - 3\sqrt{x} + 2}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{3x - 2\sqrt{x} - 1}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} - \dfrac{3\sqrt{x} - 1}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} + \dfrac{8\sqrt{x}}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{3x - 2\sqrt{x} - 1 - 3\sqrt{x} + 1 + 8\sqrt{x}}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{3x + 3\sqrt{x}}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{\bigg(\dfrac{3\sqrt{x}(\sqrt{x} + 1)}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)}\bigg)}{\dfrac{3}{3\sqrt{x} + 1}}$

$\\$

 $P = \dfrac{3\sqrt{x}(\sqrt{x} + 1)}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} : \dfrac{3}{3\sqrt{x} + 1}$

 $P = \dfrac{3\sqrt{x}(\sqrt{x} + 1)}{(3\sqrt{x} - 1)(3\sqrt{x} + 1)} . \dfrac{3\sqrt{x} + 1}{3}$

$P = \dfrac{\sqrt{x}(\sqrt{x} + 1)}{3\sqrt{x} - 1}$

b) Ta có: $P = \dfrac{\sqrt{x}(\sqrt{x} + 1)}{3\sqrt{x} - 1} = \dfrac{6}{5}$

$\Rightarrow 5\sqrt{x}(\sqrt{x} + 1) = 6(3\sqrt{x} - 1)$

$\Leftrightarrow 5x + 5\sqrt{x} = 18\sqrt{x} - 6$

$\Leftrightarrow 5x + 5\sqrt{x} -  18\sqrt{x} + 6 = 0$

$\Leftrightarrow 5x  - 13\sqrt{x} + 6 = 0$

$\Leftrightarrow (5\sqrt{x} - 3)(\sqrt{x} - 2) = 0$

$\Leftrightarrow$ \(\left[ \begin{array}{l}5\sqrt{x}-3=0\\\sqrt{x}-2=0\end{array} \right.\) 

$\Leftrightarrow$ \(\left[ \begin{array}{l}5\sqrt{x}=3\\\sqrt{x}=2\end{array} \right.\) 

$\Leftrightarrow$ \(\left[ \begin{array}{l}\sqrt{x}=\dfrac{3}{5}\\x=4\end{array} \right.\) 

$\Leftrightarrow$ \(\left[ \begin{array}{l}x = \dfrac{9}{25}\\x=4\end{array} \right.\) 

Vậy với $x = \dfrac{9}{25}$ và $x = 4$ thì $P = \dfrac{6}{5}$