Simplify the function
\[f(x) = \dfrac{(x-1)-(x-2)}{(x-1)(x-2)} + \dfrac{(x-2)-(x-3)}{(x-2)(x-3)} + \dfrac{(x-3)-(x-4)}{(x-3)(x-4)} + \dfrac{(x-4)-(x-5)}{(x-4)(x-5)}.\]
Problem
Simplify the function
\[f(x) = \dfrac{(x-1)-(x-2)}{(x-1)(x-2)} + \dfrac{(x-2)-(x-3)}{(x-2)(x-3)} + \dfrac{(x-3)-(x-4)}{(x-3)(x-4)} + \dfrac{(x-4)-(x-5)}{(x-4)(x-5)}.\]