Đáp án:

$\begin{array}{l}
Dkxd:x \ne \dfrac{4}{{11}}\\
\dfrac{{12x + 1}}{{11x - 4}} + \dfrac{{10x - 4}}{9} = \dfrac{{20x + 17}}{{18}}\\
 \Rightarrow \dfrac{{18.\left( {12x + 1} \right) + 2.\left( {10x - 4} \right).\left( {11x - 4} \right)}}{{18\left( {11x - 4} \right)}}\\
 = \dfrac{{\left( {20x + 17} \right)\left( {11x - 4} \right)}}{{18\left( {11x - 4} \right)}}\\
 \Rightarrow 216x + 18 + 2.\left( {110{x^2} - 84x + 16} \right)\\
 = 220{x^2} - 80x + 187x - 68\\
 \Rightarrow 216x + 18 + 220{x^2} - 168x + 32\\
 = 220{x^2} + 107x - 68\\
 \Rightarrow 59x = 118\\
 \Rightarrow x = 2\left( {tmdk} \right)\\
Vậy\,x = 2
\end{array}$

Đáp án:

Giải thích các bước Dkxd:x≠41112x+111x−4+10x−49=20x+1718⇒18.(12x+1)+2.(10x−4).(11x−4)18(11x−4)=(20x+17)(11x−4)18(11x−4)⇒216x+18+2.(110x2−84x+16)=220x2−80x+187x−68⇒216x+18+220x2−168x+32=220x2+107x−68⇒59x=118⇒x=2(tmdk)Vậyx=2:

Dkxd:x≠41112x+111x−4+10x−49=20x+1718⇒18.(12x+1)+2.(10x−4).(11x−4)18(11x−4)=(20x+17)(11x−4)18(11x−4)⇒216x+18+2.(110x2−84x+16)=220x2−80x+187x−68⇒216x+18+220x2−168x+32=220x2+107x−68⇒59x=118⇒x=2(tmdk)Vậyx=2