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+5) + B/(x+7). Combining gives [A(x+7)+B(x+5)]/[(x+5)(x+7)]. Matching coefficients gives A=-3, 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.