(1-x)/x - 1/x =1/x - 1 - 1/x = -1 Evaluating the expression naively near zero you're going to get wild numerical errors, but if you do the symbolic manipulati

(1-x)/x - 1/x =1/x - 1 - 1/x = -1 Evaluating the expression naively near zero you're going to get wild numerical errors, but if you do the symbolic manipulation you're going to notice that it's just equal to -1. Edit: e.g. consider this interaction I just had with the python interpreter >>> x=1e-15 >>> (1-x)/x - 1/x -1.0 >>> x=1e-16 >>> (1-x)/x - 1/x 0.0 you get completely the wrong answer when x = 1e-16