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's basically a fraction where the numerator and denominator are polynomials.

Key Concepts: Common Denominators

The goal of simplification is to find a common denominator for all the terms in the expression. This allows you to combine like terms and reduce the expression to its simplest form.

Steps for Simplification:

1. Find the Least Common Multiple (LCM) of the denominators. This is the smallest number that all the denominators divide into evenly.
2. Multiply each term by the reciprocal of the denominator. This creates a common denominator.
3. Simplify the resulting expression. Combine like terms to get the final, simplified form.

Example: Simplify: (2x / (x+1)) + (3x / (x+1))

1. LCM of (x+1) is (x+1).
2. Multiply by (x+1)/ (x+1): (2x + 3x) / (x+1) = 5x / (x+1)

Important Note: You can only simplify by combining like terms!