[tex]e(x) = \frac{x}{x {}^{2} + x } - ( \frac{x}{x - 1} - \frac{x}{x + 1}) \div \frac{2x}{x - 1} \\ e(x) = \frac{x}{x(x + 1)} - \frac{x(x + 1) - x(x - 1)}{(x + 1)(x - 1)} \times \frac{x - 1}{2x} \\ e(x) = \frac{1}{x + 1} - \frac{x {}^{2} + x - x {}^{2} + x }{x + 1} \times \frac{1}{2x} \\ e(x) = \frac{1}{x + 1} - \frac{2x}{x + 1} \times \frac{1}{2x} \\ e(x) = \frac{1}{x + 1} - \frac{1}{x + 1} \\ e(x) = \frac{1 - 1}{x + 1} \\ e(x) = \frac{0}{x + 1} \\ e(x) = 0[/tex]
