Đáp án:
$\begin{array}{l}
Dkxd:x \ne - 1;x \ne 3\\
\frac{x}{{2\left( {x - 3} \right)}} + \frac{x}{{2x + 2}} = \frac{{2x}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
\Rightarrow \frac{{x\left( {x + 1} \right) + x\left( {x - 3} \right)}}{{2\left( {x - 3} \right)\left( {x + 1} \right)}} = \frac{{2x}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
\Rightarrow \frac{{{x^2} + x + {x^2} - 3x}}{{2\left( {x - 3} \right)\left( {x + 1} \right)}} = \frac{{4x}}{{2\left( {x + 1} \right)\left( {x - 3} \right)}}\\
\Rightarrow 2{x^2} - 2x = 4x\\
\Rightarrow {x^2} - 3x = 0\\
\Rightarrow x\left( {x - 3} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 0\left( {tm} \right)\\
x = 3\left( {ktm} \right)
\end{array} \right.\\
Vậy\,x = 0\\
\frac{{4x - 3}}{5} - \frac{{6x - 2}}{7} = \frac{{5x + 4}}{3} + 3\\
\Rightarrow \frac{{21\left( {4x - 3} \right) - 15\left( {6x - 2} \right) - 35\left( {5x + 4} \right) - 3.105}}{{105}} = 0\\
\Rightarrow 84x - 62 - 90x + 30 - 175x - 140 - 315 = 0\\
\Rightarrow - 181x - 487 = 0\\
\Rightarrow x = - \frac{{497}}{{181}}
\end{array}$
