Chapter 7 - Principles Of Integral Evaluation - 7.5 Integrating Rational Functions By Partial Fractions - Exercises Set 7.5 - Page 521: 1

$$\frac{A}{{x - 3}} + \frac{B}{{x + 4}}$$

$$\eqalign{ & \frac{{3x - 1}}{{\left( {x - 3} \right)\left( {x + 4} \right)}} \cr & {\text{The factors in the denominator }}x - 3{\text{ and }}x + 4{\text{ are linear}}{\text{, }} \cr & {\text{so the numerator for each factor is a constant}}{\text{.}} \cr & {\text{The partial fraction decomposition is in the form:}} \cr & \frac{{3x - 1}}{{\left( {x - 3} \right)\left( {x + 4} \right)}} = \frac{A}{{x - 3}} + \frac{B}{{x + 4}} \cr} $$