Because the denominator is a product of two different linear factors, split the fraction into two simpler fractions, one over each factor. Assume A/(x+3) + B/(x+5). Combining gives [A(x+5)+B(x+3)]/[(x+3)(x+5)]. Matching coefficients gives A=6, B=-5. In practice, compare the coefficient of x and the constant term on both sides to find A and B. After A and B are found, place them above their matching denominators to get the partial fraction form.