Thực hiện phép tính sau: $\Large \left( \dfrac{2x}{3x+1}-1 \right):\le

Thực hiện phép tính sau: $\Large \left( \dfrac{2x}{3x+1}-1 \right):\left( 1-\dfrac{8{{x}^{2}}}{9{{x}^{2}}-1} \right)$, ta được kết quả là:

• A. $\dfrac{1-3x}{x-1}$
• B. $\dfrac{3x-1}{x-1}$
• C. $\dfrac{-\left( 3x+1 \right)}{x-1}$
• D. $\dfrac{1-3x}{-x-1}$

Đkxđ:

$\Large \left\{ \begin{array}{l} & 3x+1\ne 0 \\  & 9{{x}^{2}}-1\ne 0 \\ \end{array} \right.\Leftrightarrow \left\{ \begin{array}{l} & 3x+1\ne 0 \\  & \left( 3x-1 \right)\left( 3x+1 \right)\ne 0 \\ \end{array} \right.\Leftrightarrow x\ne \pm \dfrac {1}{3}$

$\Large  \begin{align}  &\left( \dfrac{2x}{3x+1}-1 \right):\left( 1-\dfrac{8{{x}^{2}}}{9{{x}^{2}}-1} \right) \\  & =\left( \dfrac{2x-3x-1}{3x+1} \right):\left( \dfrac{9{{x}^{2}}-1-8{{x}^{2}}}{9{{x}^{2}}-1} \right) \\  & =\dfrac{-x-1}{3x+1}:\dfrac{{{x}^{2}}-1}{9{{x}^{2}}-1} \\  & =\dfrac{-x-1}{3x+1}.\dfrac{9{{x}^{2}}-1}{{{x}^{2}}-1} \\  & =\dfrac{-\left( x+1 \right)}{3x+1}.\dfrac{\left( 3x+1 \right)\left( 3x-1 \right)}{\left( x+1 \right)\left( x-1 \right)} \\  & =\dfrac{1-3x}{x-1} \\ \end{align}$