Year 10: Addition and subtraction of rational expressions

Key concepts

• Common denominator: The most crucial step! You MUST have a common denominator before adding or subtracting.
• Finding the LCM: The least common multiple (LCM) of the denominators is often the required common denominator.
• Simplifying: Always simplify your answer to its simplest form.

Rules

1. Addition:

   To add rational expressions with the same denominator, add the numerators and keep the denominator.

   $a/b+c/b=(a+c)/b$

2. Subtraction:

   To subtract rational expressions with the same denominator, subtract the numerators and keep the denominator.

   $a/b-c/b=(a-c)/b$

Steps

1. Identify the Denominators: Find the denominators of the rational expressions.
2. Find the LCM: Calculate the least common multiple (LCM) of the denominators.
3. Create a Common Denominator: Rewrite each rational expression with the LCM as the denominator.
4. Add/Subtract Numerators: Add or subtract the numerators, keeping the common denominator.
5. Simplify: Simplify the resulting rational expression.