Quick Review Quiz: Simplify Rational Expressions (Algebra 2)

📚 Quick Study Guide

• 🔍 Rational Expression: A fraction where the numerator and/or denominator are polynomials. Example: $\frac{x^2 + 2x + 1}{x + 1}$
• 💡 Simplifying: The goal is to cancel out common factors from the numerator and denominator.
• 📝 Factoring is Key: Before you can cancel anything, you need to factor both the numerator and the denominator.
• ➗ Division: To divide rational expressions, flip the second fraction and multiply.
• 🚫 Restrictions: Always state the values of the variable that would make the denominator zero (undefined).
• ➕ Adding/Subtracting: Requires a common denominator. Find the least common multiple (LCM) of the denominators.
• 🧮 Example: Simplify $\frac{x^2 - 4}{x^2 + 4x + 4}$. Factor to get $\frac{(x-2)(x+2)}{(x+2)(x+2)}$. Cancel $(x+2)$ to get $\frac{x-2}{x+2}$, $x \neq -2$.

🧪 Practice Quiz

1. What is the simplified form of $\frac{4x^2y}{6xy^3}$?
   1. $\frac{2x}{3y^2}$
   2. $\frac{3y^2}{2x}$
   3. $\frac{2}{3xy^2}$
   4. $\frac{2x}{3y}$
2. Simplify: $\frac{x^2 - 9}{x + 3}$
   1. $x - 3$
   2. $x + 3$
   3. $\frac{1}{x+3}$
   4. $\frac{1}{x-3}$
3. Simplify: $\frac{x^2 + 5x + 6}{x^2 + 4x + 4}$
   1. $\frac{x+3}{x+2}$
   2. $\frac{x+2}{x+3}$
   3. $\frac{5x+6}{4x+4}$
   4. $\frac{3}{2}$
4. What is the simplified form of $\frac{2x}{x^2-4} \cdot \frac{x+2}{4x^2}$?
   1. $\frac{1}{2x(x-2)}$
   2. $\frac{1}{2x(x+2)}$
   3. $\frac{2x}{x-2}$
   4. $\frac{1}{x(x-2)}$
5. Simplify: $\frac{x^2 - 1}{x+1} \div \frac{x-1}{x}$
   1. $x$
   2. $\frac{1}{x}$
   3. $x^2$
   4. 1
6. Simplify: $\frac{x}{x+1} + \frac{1}{x+1}$
   1. 1
   2. $\frac{x+1}{x+1}$
   3. $\frac{x+2}{x+1}$
   4. $\frac{x}{x+1}$
7. Simplify: $\frac{x}{x-2} - \frac{2}{x-2}$
   1. 1
   2. $\frac{x-2}{x-2}$
   3. $\frac{x+2}{x-2}$
   4. $\frac{x}{x-2}$