JEE Math Practice Question

If f(x) is a differentiable function in the interval (0, $$\infty $$) such that f (1) = 1 and $$\mathop {\lim }\limits_{t \to x} $$ $${{{t^2}f\left( x \right) - {x^2}f\left( t \right)} \over {t - x}} = 1,$$ for each x > 0, then $$f\left( {{3/2}} \right)$$ equal to :

1. A.$${{13} \over 6}$$
2. B.$${{23} \over 18}$$
3. C.$${{25} \over 9}$$
4. D.$${{31} \over 18}$$