Question

Write as a sum of partial fractions. x/(3x-2)(2x+1)

Answer 1

\[\begin{align*}\frac{x}{(3x-2)(2x+1)}&=\frac{A}{3x-2}+\frac{B}{2x+1}\\
x&=A(2x+1)+B(3x-2)\\
x&=(2A+3B)x+A-2B
\end{align*}\]
This gives you the system
\[\begin{cases}2A+3B=1\\
A-2B=0\end{cases}\]
Solve for \(A\) and \(B\).