Step-by-step explanation:
[tex]\frac{2x + 1}{(x + 2)(x - 3)} \equiv \frac{A}{(x - 3)} + \frac{ B}{(x + 2)} \\ \\ 2x + 1 \equiv \: A(x + 2) + B(x - 3) \\ 2x + 1 \equiv \: Ax + 2A + Bx - 3B \\A + B = 2...(1) \\ 2A - 3B = 1...(2) \\ A = \frac{7}{5} \: and \: B = \frac{3}{5} \\ \frac{2x + 1}{(x + 2)(x - 3)} \equiv \frac{\frac{7}{5}}{(x - 3)} + \frac{ \frac{3}{5} }{(x + 2)}[/tex]
