Mathematics

The key is to recognize that the denominator has one linear factor and one irreducible quadratic, so you'll need both a constant term over the linear part and a linear numerator over the quadratic. Set up $\frac{A}{3x+2} + \frac{Bx+C}{4x^2+5x+6}$, then multiply through by the full denominator to match coefficients on both sides. This turns a tricky rational expression into a simple system of equations.

The key is to recognize that the denominator has one linear factor and one irreducible quadratic, so you'll need both a constant term over the linear part and a linear numerator over the quadratic. Set up $\frac{A}{3x+2} + \frac{Bx+C}{4x^2+5x+6}$, then multiply through by the full denominator to match coefficients on both sides. This turns a tricky rational expression into a simple system of equations.