Year 10: Simplification of rational algebraic expressions

What is a Rational Algebraic Expression?

A rational algebraic expression is an expression that can be written as a fraction where the numerator and denominator are polynomials. It's essentially a fraction involving variables and exponents. Example: (x² + 2x) / (x + 1)

Steps to Simplify

1. Factor the numerator and denominator separately: This is the MOST important step. Find the greatest common factor (GCF) of all terms.
2. Cancel Common Factors: Once factored, identify and cancel out any factors that appear in both the numerator and denominator.
3. Check for Extraneous Solutions (If Applicable): This is crucial when dealing with rational equations. Ensure you're not cancelling factors that would make the denominator zero, leading to undefined expressions.

Examples

Example 1: Simplify (x² - 9) / (x + 3)

1. Factor: (x + 3)(x - 3)

2. Cancel: (x - 3)

Result: x - 3

Example 2: Simplify (2x² + 6x) / (x² - 1)

1. Factor: 2(x + 3)(x - 1)

2. Cancel: (2(x - 1))

Result: 2(x - 1)

Important Notes

• Always simplify before any calculations.
• Be careful when factoring. Mistakes in factoring lead to incorrect simplification.
• Remember that you can only cancel factors that are in both the numerator and denominator.