Đáp án:
$\begin{array}{l}
a)\dfrac{{3x - 2}}{{x + 7}} = \dfrac{{6x + 1}}{{2x - 3}}\\
Dk:x \ne - 7;x \ne \dfrac{3}{2}\\
\Rightarrow \left( {3x - 2} \right).\left( {2x - 3} \right) = \left( {x + 7} \right)\left( {6x + 1} \right)\\
\Rightarrow 6{x^2} - 9x - 4x + 6 = 6{x^2} + x + 42x + 7\\
\Rightarrow 43x + 13x = 6 - 7\\
\Rightarrow 56x = - 1\\
\Rightarrow x = - \dfrac{1}{{56}}\left( {tmdk} \right)\\
\text{Vậy}\,x = \dfrac{{ - 1}}{{56}}\\
h)\dfrac{{x + 1}}{{x - 2}} - \dfrac{{x - 1}}{{x + 2}} = \dfrac{{2\left( {{x^2} + 2} \right)}}{{{x^2} - 4}}\\
Dkxd:x \ne 2;x \ne - 2\\
\Rightarrow \dfrac{{\left( {x + 1} \right)\left( {x + 2} \right) - \left( {x - 1} \right)\left( {x - 2} \right)}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\\
= \dfrac{{2{x^2} + 4}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\\
\Rightarrow {x^2} + 3x + 2 - \left( {{x^2} - 3x + 2} \right) = 2{x^2} + 4\\
\Rightarrow 6x = 2{x^2} + 4\\
\Rightarrow {x^2} - 3x + 2 = 0\\
\Rightarrow \left( {x - 1} \right)\left( {x - 2} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 1\left( {tm} \right)\\
x = 2\left( {ktm} \right)
\end{array} \right.\\
\text{Vậy}\,x = 1\\
j)\dfrac{{2x + 1}}{{x - 1}} = \dfrac{{5\left( {x - 1} \right)}}{{x + 1}}\\
Dkxd:x \ne 1;x \ne - 1\\
\Rightarrow \left( {2x + 1} \right)\left( {x + 1} \right) = 5\left( {x - 1} \right)\left( {x - 1} \right)\\
\Rightarrow 2{x^2} + 3x + 1 = 5\left( {{x^2} - 2x + 1} \right)\\
\Rightarrow 3{x^2} - 13x + 4 = 0\\
\Rightarrow \left( {3x - 1} \right)\left( {x - 4} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = \dfrac{1}{3}\left( {tm} \right)\\
x = 4\left( {tm} \right)
\end{array} \right.\\
\text{Vậy}\,x = \dfrac{1}{3};x = 4\\
j)\dfrac{{x - 1}}{{x + 2}} - \dfrac{x}{{x - 2}} = \dfrac{{5x - 2}}{{4 - {x^2}}}\\
DKxd:x \ne 2;x \ne - 2\\
\Rightarrow \dfrac{{\left( {x - 1} \right)\left( {x - 2} \right) - x\left( {x + 2} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} = \dfrac{{2 - 5x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
\Rightarrow {x^2} - 3x + 2 - {x^2} - 2x = 2 - 5x\\
\Rightarrow 2 - 5x = 2 - 5x\\
\text{Vậy phương trình đúng với mọi x#2;x#-2}
\end{array}$
