Complex Fractions B58B64

1. **Problem Statement:** Simplify the given complex fraction or rational expression. 2. **Formula and Rules:** To simplify complex fractions, use the rule: $$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$. Also, simplify rational expressions by factoring numerators and denominators and canceling common factors. 3. **Step-by-step Solution:** - Identify the numerator and denominator of the complex fraction. - Rewrite the complex fraction as a multiplication by the reciprocal. - Factor numerator and denominator if possible. - Cancel common factors using \cancel{} notation. - Simplify the resulting expression. 4. **Example:** Suppose the expression is $$\frac{\frac{2x}{3}}{\frac{4}{9x}}$$. - Rewrite as $$\frac{2x}{3} \times \frac{9x}{4}$$. - Multiply numerators and denominators: $$\frac{2x \times 9x}{3 \times 4} = \frac{18x^2}{12}$$. - Simplify fraction: $$\frac{\cancel{18}x^2}{\cancel{12}} = \frac{3x^2}{2}$$. 5. **Final Answer:** $$\frac{3x^2}{2}$$. This method applies to any complex fraction or rational expression to simplify it effectively.