Year 8: 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 of two polynomials. It looks like this: (Polynomial) / (Polynomial)

Simplifying Rational Algebraic Expressions

Simplifying means making the expression easier to understand and work with. Here's how:

1. Factorise the Numerator and Denominator

This is the most important step! Find the highest common factor (HCF) of the numerator and denominator.

2. Cancel Common Factors

After factorising, if a factor appears in both the numerator and denominator, you can cancel it out. Remember that you can only cancel out factors, not numbers!

3. Check for Further Simplification

Sometimes, after cancelling, you might be able to simplify further.

Example:

Simplify: (x² + 2x) / (x + 2)

Step 1: Factorise the numerator: (x)(x + 2)

Step 2: Cancel the common factor (x + 2): x / 1 = x

Therefore, the simplified expression is x