Đáp án:
\(\left\{ \begin{array}{l}
a = 1\\
b = - 5
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{x + 5}}{{{x^2} - 25}} = \dfrac{{ax + b}}{{{x^2} - 10x + 25}}\\
VT = \dfrac{{x + 5}}{{{x^2} - 25}} = \dfrac{{x + 5}}{{\left( {x + 5} \right)\left( {x - 5} \right)}} = \dfrac{1}{{x - 5}}\\
VP = \dfrac{{ax + b}}{{{{\left( {x - 5} \right)}^2}}}\\
VT = VP \Leftrightarrow ax + b = x - 5\\
\to \left\{ \begin{array}{l}
a = 1\\
b = - 5
\end{array} \right.
\end{array}\)
