$$a * b = \frac{a^2 + b^2}{ab}, a > 0, b > 0 \Rightarrow \frac{(1 * 2) * (1 * 1)}{1 * 3} =$$

A

$$\frac{111}{10}$$

B

$$\frac{121}{100}$$

C

$$\frac{123}{150}$$

D

$$\frac{123}{200}$$