You can only use the usual rule for finding A and B when the numerator of the original fraction is of the form cx+d (where c and d are constants). In this case, numerator is \(\displaystyle -e^{-x}\), which is obviously not of that form. So you have to extract that numerator, and write the fraction as \(\displaystyle -e^{-x}\frac1{x(x+1)}\). Then apply the usual partial fractions procedure to get \(\displaystyle \frac1{x(x+1)} = \frac1x - \frac1{x+1}\). Finally, bring back the factor \(\displaystyle -e^{-x}\) to get \(\displaystyle \frac{-e^{-x}}{x(x+1)} = \frac{-e^{-x}}x - \frac{-e^{-x}}{x+1}\).