Year 10: Simplification of rational algebraic expressions

This cheat sheet covers simplifying rational algebraic expressions (fractions with polynomials) in Year 10 Algebra.

Key Concepts

• Rational Expression: An expression that can be written as a fraction where the numerator and denominator are polynomials.
• Simplifying: Reducing a rational expression to its simplest form, meaning the numerator and denominator have no common factors.

Steps for Simplification

1. Factor the Numerator and Denominator: Factor each polynomial expression fully. This is crucial!
2. Identify Common Factors: Look for factors that appear in both the numerator and denominator.
3. Cancel Common Factors: Divide out any common factors. Remember, you're dividing by a factor, not plugging it in.
4. Check for Extraneous Solutions: After simplifying, make sure your solution makes the original denominator zero. If it does, the solution is extraneous and invalid.

Examples

Example 1: (x² - 9) / (x + 3)

Factor: ((x+3)(x-3)) / (x+3)

Cancel: x - 3

Example 2: (x² + 5x + 6) / (x + 2)

Factor: (x+2)(x+3) / (x+2)

Cancel: x + 3