Set up the partial fraction decomposition of 3x+1(x−1)(x+2)\dfrac{3x + 1}{(x-1)(x+2)}(x−1)(x+2)3x+1.
Ax−1+Bx+2\dfrac{A}{x-1} + \dfrac{B}{x+2}x−1A+x+2B
Ax+Bx−1+Cx+2\dfrac{Ax+B}{x-1} + \dfrac{C}{x+2}x−1Ax+B+x+2C
A(x−1)(x+2)+B\dfrac{A}{(x-1)(x+2)} + B(x−1)(x+2)A+B
A+Bx−1A + \dfrac{B}{x-1}A+x−1B