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+1) + B/(x+8). Combining gives [A(x+8)+B(x+1)]/[(x+1)(x+8)]. Matching coefficients gives A=-1, B=4. 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.