Chapter 7 - Techniques of Integration - 7.4 Integration of Rational Functions by Partial Fractions - 7.4 Exercises - Page 541: 2

a) $\frac{A}{x-2}+\frac{B}{x+3}$ b) $1-\frac{Ax+B}{x^{2}+x+6}$

a) $\frac{x-6}{x^{2}+x-6}$ = $\frac{x-6}{(x+3)(x-2)}$ = $\frac{A}{x-2}+\frac{B}{x+3}$ b) $\frac{x^2}{x^{2}+x+6}$ = $1-\frac{x+6}{x^{2}+x+6}$ = $1-\frac{Ax+B}{x^{2}+x+6}$