\(\dfrac {2x - 18}{(x + 3)(x - 2)} = \dfrac {A}{x + 3} + \dfrac {B}{x - 1}\)
(1) menyetarakan penyebut
\(\dfrac {2x - 18}{(x + 3)(x - 2)} = \dfrac {A(x - 1) + B(x + 3)}{(x + 3)(x - 2)}\)
(2) menyamakan pembilang
Karena penyebut sudah sama, maka kita bisa samakan bagian pembilang
\(2x - 18 = A(x - 1) + B(x + 3)\)
(3) substitusi bilangan yang sesuai
Substitusi \(x = 1\) akan mendapatkan nilai B
\begin{equation*}
\begin{split}
A(x - 1) + B(x + 3) & = 2x - 18 \\\\
A(1 - 1) + B(1 + 3) & = 2 \:.\: 1 - 18 \\\\
4B & = -16 \\\\
B & = -4
\end{split}
\end{equation*}
Substitusi \(x = -3\) akan mendapatkan nilai A
\begin{equation*}
\begin{split}
A(x - 1) + B(x + 3) & = 2x - 18 \\\\
A(-3 - 1) + B(-3 + 3) & = 2 \:.\: -3 - 18 \\\\
-4A & = -24 \\\\
A & = 6
\end{split}
\end{equation*}
\(\dfrac {2x - 18}{(x + 3)(x - 2)} = \dfrac {6}{x + 3} - \dfrac {4}{x - 1}\)
Alternatif cara lain
\begin{equation*}
\begin{split}
A(x - 1) + B(x + 3) & = 2x - 18 \\\\
Ax - A + Bx + 3B & = 2x - 18 \\\\
(A + B)x - A + 3B & = 2x - 18
\end{split}
\end{equation*}
Maka \(A + B = 2\) dan \(-A + 3B = -18\)
Eliminasi kedua persamaan akan mendapatkan nilai A dan B
\begin{equation*}
\begin{split}
A + B & = 2 \\\\
-A + 3B & = -18 \quad(+) \\
\hline\\
4B & = -16 \\\\
B & = -4 \\\\
A & = 6
\end{split}
\end{equation*}
\(\dfrac {2x - 18}{(x + 3)(x - 2)} = \dfrac {6}{x + 3} - \dfrac {4}{x - 1}\)