Year 9: Addition and subtraction of rational expressions

Key Concepts

Adding and subtracting rational expressions (fractions with polynomials) requires a common denominator.

Common Denominator: The least common multiple (LCM) of the denominators.

Steps for addition and subtraction

1. Find the Least common denominator (LCD): Calculate the LCM of all denominators.
2. Rewrite the rational expressions: Rewrite each rational expression with the LCD as the denominator.
3. Add or subtract the numerators: Add or subtract the numerators, keeping the LCD.
4. Simplify: Simplify the resulting rational expression by dividing the numerator and denominator by their greatest common factor (GCF).

Important rules

• Adding/subtracting like terms: Like terms must have the same denominator before adding or subtracting.
• Simplifying: Always simplify the resulting rational expression.

Example

1/(x+2) + 2/(x+2) = (1+2)/(x+2) = 3/(x+2)