Phương trình $\Large \dfrac{3}{1-4x}=\dfrac{2}{4x+1}-\dfrac{8+6x}{16{{

Phương trình $\Large \dfrac{3}{1-4x}=\dfrac{2}{4x+1}-\dfrac{8+6x}{16{{x}^{2}}-1}$ có nghiệm là:

• A. $\Large x=\dfrac{1}{2}$
• B. $\Large x=2$
• C. $\Large x=1$
• D. $\Large x=3$

ĐKXĐ: $\Large x\ne \pm \dfrac{1}{4}$

$\Large \begin{align}& \Leftrightarrow \dfrac{-3\left( 4x+1 \right)}{\left( 4x-1 \right)\left( 4x+1 \right)}=\dfrac{2\left( 4x-1 \right)}{\left( 4x-1 \right)\left( 4x+1 \right)}-\dfrac{8+6x}{\left( 4x-1 \right)\left( 4x+1 \right)} \\  & \Rightarrow -3\left( 4x+1 \right)=2\left( 4x-1 \right)-\left( 8+6x \right) \\ & \Leftrightarrow -12x-3=8x-2-8-6x \\  & \Leftrightarrow -12x-8x+6x=-2-8+3 \\  & \Leftrightarrow -14x=-7\Leftrightarrow x=\dfrac{1}{2}\left( tm \right) \\ \end{align}$

Vậy phương trình nghiệm $\Large x=\dfrac{1}{2}$