Assessment Questions

1. Simplify: \(\frac{2x^2}{3x} \cdot \frac{9x^3}{4}\)
2. Add/Subtract: \(\frac{3}{x+2} + \frac{5}{x+2}\)
3. Solve: \(\frac{x}{x-1} + \frac{2}{x-1} = 5\)
4. Multiply/Divide: \(\frac{2x}{x+3} \div \frac{4}{x+3}\)
5. Complex fraction: \(\frac{\frac{1}{x} + 2}{\frac{3}{x}}\)
6. Application: A tank is filled by two pipes. Pipe A fills in 4 h, pipe B in 6 h. How long together?
7. Solve rational equation: \(\frac{3}{x} + \frac{2}{x+1} = 1\)
8. Word problem: A car rental charges $25/day plus $0.15/mile. Total $85 for 200 miles. Find days rented.
9. Real-life: Combine 5% and 15% solutions to make 12 L of 10% solution. How much of each?
10. Graphing: Identify asymptotes and domain for \(f(x) = \frac{2x+1}{x-3}\)