tìm a, b thỏa mãn x khác 5 x khác 4: 5x-2/x ² +x-20=a/x+5-b/x+4

Đáp án:

$\begin{array}{l}
\dfrac{{5x – 2}}{{{x^2} + x – 20}} = \dfrac{a}{{x + 5}} – \dfrac{b}{{x – 4}}\\
 \Rightarrow \dfrac{{5x – 2}}{{{x^2} + 5x – 4x – 20}} = \dfrac{{a\left( {x – 4} \right) – b\left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x – 4} \right)}}\\
 \Rightarrow \dfrac{{5x – 2}}{{\left( {x + 5} \right)\left( {x – 4} \right)}} = \dfrac{{a.x – 4a – b.x – 5b}}{{\left( {x + 5} \right)\left( {x – 4} \right)}}\\
 \Rightarrow 5x – 2 = \left( {a – b} \right).x – 4a – 5b\\
 \Rightarrow \left\{ \begin{array}{l}
5 = a – b\\
 – 2 =  – 4a – 5b
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
a – b = 5\\
4a + 5b = 2
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
4a – 4b = 20\\
4a + 5b = 2
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
9b =  – 18\\
a = 5 + b
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
b =  – 2\\
a = 3
\end{array} \right.\\
Vậy\,a = 3;b =  – 2
\end{array}$