Đáp án: $a = \frac{{ - 2}}{5};b = \frac{2}{5}$
Giải thích các bước giải:
$\begin{array}{l}
\frac{2}{{\left( {x + 2} \right).\left( {x - 3} \right)}} = \frac{a}{{x + 2}} + \frac{b}{{x - 3}}\\
\Rightarrow \frac{2}{{\left( {x + 2} \right).\left( {x - 3} \right)}} = \frac{{a\left( {x - 3} \right) + b\left( {x + 2} \right)}}{{\left( {x + 2} \right).\left( {x - 3} \right)}}\\
\Rightarrow \frac{2}{{\left( {x + 2} \right).\left( {x - 3} \right)}} = \frac{{\left( {a + b} \right)x - 3a + 2b}}{{\left( {x + 2} \right).\left( {x - 3} \right)}}\\
\Rightarrow 2 = \left( {a + b} \right).x - 3a + 2b\\
\Rightarrow \left\{ \begin{array}{l}
a + b = 0\\
- 3a + 2b = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - b\\
- 3.\left( { - b} \right) + 2b = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - b\\
5b = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - b\\
b = \frac{2}{5}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = \frac{{ - 2}}{5}\\
b = \frac{2}{5}
\end{array} \right.
\end{array}$
