Mixed Problems

1. Simplify: \(\dfrac{x^2 - 4}{x^2 - 2x}\)
2. Multiply: \(\dfrac{2x}{3} \cdot \dfrac{9}{4x}\)
3. Add: \(\dfrac{1}{x} + \dfrac{2}{x+1}\)
4. Complex fraction: \(\dfrac{\tfrac{1}{a}+\tfrac{1}{b}}{\tfrac{1}{a}}\)
5. Solve equation: \(\dfrac{3}{x} - \dfrac{2}{x+1} = 1\)
6. Word problem: A faucet fills a tank in 6 hours, another in 4 hours. How long together?
7. Simplify: \(\dfrac{y^2 - 9}{y^2 - 6y + 9}\)
8. Divide: \(\dfrac{x^2 - 16}{x+4} \div \dfrac{x-4}{x}\)
9. Solve: \(\dfrac{x}{x+2} + \dfrac{2}{x} = 3\)
10. Application: A car travels 100 miles downstream in 2 hours, back upstream in 5 hours. Find boat and current speed.