Giải thích các bước giải:
ĐK:$x \ne \left\{ {1;2;3} \right\}$
Ta có:
$\begin{array}{l}
\dfrac{1}{{\left( {x - 1} \right)\left( {x - 2} \right)}} + \dfrac{2}{{\left( {2 - x} \right)\left( {3 - x} \right)}} + \dfrac{3}{{\left( {1 - x} \right)\left( {3 - x} \right)}}\\
= \dfrac{1}{{\left( {x - 1} \right)\left( {x - 2} \right)}} + \dfrac{2}{{\left( {x - 2} \right)\left( {x - 3} \right)}} + \dfrac{3}{{\left( {x - 1} \right)\left( {x - 3} \right)}}\\
= \dfrac{{x - 3 + 2\left( {x - 1} \right) + 3\left( {x - 2} \right)}}{{\left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)}}\\
= \dfrac{{6x - 11}}{{\left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)}}
\end{array}$
