Question

Dada a função f(x) = 1/x, calcule f(x)-f(a)/x-a

Answer 1

$\frac{f(x) - f(a)}{x - a} = \frac{ \frac{1}{x} - \frac{1}{a} }{x - a} = \frac{ \frac{a - x}{ax} }{x - a} = \\ = \frac{a - x}{ax} \times \frac{1}{x - a} = \frac{a - x}{ax(x - a)} = \\ = \frac{ - (x - a)}{ax(x - a)} = - \frac{1}{ax}$