If $$x^2 - 5\sqrt{2}x + 1 = 0$$, then what is the value of $$\frac{\left(x^3 + \frac{1}{x}\right)}{x^2 + 1} ?$$

A

$$\frac{24\sqrt{2}}{5}$$

B

$$\frac{12\sqrt{2}}{5}$$

C

$$\frac{18\sqrt{2}}{5}$$

D

$$\frac{26\sqrt{2}}{5}$$