Giải thích các bước giải:
$\begin{array}{l}
+ )6x - 3y - 4{x^2} + 4xy - {y^2}\\
= 3\left( {2x - y} \right) - \left( {4{x^2} - 4xy + {y^2}} \right)\\
= 3\left( {2x - y} \right) - {\left( {2x - y} \right)^2}\\
= \left( {2x - y} \right)\left( {3 - 2x + y} \right)\\
= \left( {2x - y} \right)\left( { - 2x + y + 3} \right)\\
+ )\\
\frac{{2x + 3}}{{{x^2} - 5x + 6}} = \frac{m}{{x - 2}} + \frac{n}{{x - 3}}\\
\Rightarrow \frac{{2x + 3}}{{\left( {x - 2} \right)\left( {x - 3} \right)}} = \frac{{m\left( {x - 3} \right) + n\left( {x - 2} \right)}}{{\left( {x - 2} \right)\left( {x - 3} \right)}}\\
\Rightarrow 2x + 3 = mx - 3m + nx - 2n\\
\Rightarrow 2x + 3 = \left( {m + n} \right)x + \left( { - 3m - 2n} \right)\\
\Rightarrow \left\{ \begin{array}{l}
m + n = 2\\
- 3m - 2n = 3
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m = - 7\\
n = 9
\end{array} \right.
\end{array}$
