Let f(x) be differentiable on the interval $$(0, \infty)$$ suh that f(1) = 1, and $$\lim_{t \rightarrow x}\frac{t^2 f(x) - x^2f(t)}{t-x} = 1$$ for each x > 0. Then f(x) is

A

$$\frac{1}{3x}+\frac{2x^2}{3}$$

B

$$\frac{-1}{3x}+\frac{4x^2}{3}$$

C

$$\frac{-1}{x}+\frac{2}{x^2}$$

D

$$\frac{1}{x}$$