Simplify: (3 1/2 + 2 1/4) ÷ (5 2/3 - 1 1/2). (b) Solve for n in the equation 2n² = 4n.

Convert mixed numbers to improper fractions and find a common denominator.

$$3\frac{1}{2} + 2\frac{1}{4} = \frac{7}{2} + \frac{9}{4}$$ $$= \frac{14}{4} + \frac{9}{4} = \frac{14+9}{4} = \frac{23}{4}$$

Convert mixed numbers to improper fractions and find a common denominator.

$$5\frac{2}{3} - 1\frac{1}{2} = \frac{17}{3} - \frac{3}{2}$$ $$= \frac{34}{6} - \frac{9}{6} = \frac{34-9}{6} = \frac{25}{6}$$

To divide by a fraction, multiply by its reciprocal.

$$\frac{23}{4} \div \frac{25}{6} = \frac{23}{4} \times \frac{6}{25}$$ $$= \frac{23 \times 6}{4 \times 25} = \frac{138}{100}$$

$$\frac{138}{100} = \frac{69}{50}$$ $$= 1\frac{19}{50}$$

The simplified expression is $\boxed{1\frac{19}{50}}$.

2. (b) Solve for $n$ in the equation $2n^2 = 4n$.

$$2n = 0 \quad \text{or} \quad n - 2 = 0$$ $$n = \frac{0}{2} \quad \text{or} \quad n = 2$$ $$n = 0 \quad \text{or} \quad n = 2$$

The solutions for $n$ are $\boxed{n=0 \text{ or } n=2}$.