Express $\dfrac{3x^2 + x + 2}{(x^2 + 1)(x - 1)}$ in partial fractions.

Let (3x²+x+2)/[(x²+1)(x-1)] = (Ax+B)/(x²+1) + C/(x-1). Multiplying through: 3x²+x+2 = (Ax+B)(x-1) + C(x²+1). Setting x=1: 6 = 2C, so C=3. Expanding and comparing coefficients of x²: A+C=3, so A=0... Comparing constants: -B+C=2, so B=1. Comparing x terms: A-B=1, so A=2. Thus partial fractions = (2x-1)/(x²+1) + 3/(x-1).