Simplify: 3 3/10 - 1 2/3 / 1 1/2 + 1/10

$$3\frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{33}{10}$$ $$1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$$ $$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$$

The expression becomes:

$$\frac{\frac{33}{10} - \frac{5}{3}}{\frac{3}{2} + \frac{1}{10}}$$

To subtract $\frac{5}{3}$ from $\frac{33}{10}$, find a common denominator, which is 30.

$$\frac{33}{10} - \frac{5}{3} = \frac{33 \times 3}{10 \times 3} - \frac{5 \times 10}{3 \times 10} = \frac{99}{30} - \frac{50}{30} = \frac{99 - 50}{30} = \frac{49}{30}$$

To add $\frac{3}{2}$ and $\frac{1}{10}$, find a common denominator, which is 10.

$$\frac{3}{2} + \frac{1}{10} = \frac{3 \times 5}{2 \times 5} + \frac{1}{10} = \frac{15}{10} + \frac{1}{10} = \frac{15 + 1}{10} = \frac{16}{10}$$

This fraction can be simplified by dividing both numerator and denominator by 2:

$$\frac{16}{10} = \frac{8}{5}$$

$$\frac{\frac{49}{30}}{\frac{8}{5}}$$

To divide by a fraction, multiply by its reciprocal:

$$\frac{49}{30} \times \frac{5}{8}$$

Multiply the numerators and the denominators:

$$\frac{49 \times 5}{30 \times 8}$$

Simplify by canceling out common factors. Here, 5 divides into 30 six times:

$$\frac{49 \times 1}{6 \times 8} = \frac{49}{48}$$

The simplified expression is $\frac{49}{48}$.