Year 10: Addition and subtraction of rational expressions

Key Concepts

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

Common Denominator

• Finding a Common Denominator: The least common multiple (LCM) of the denominators is often the easiest choice.
• LCM Calculation: To find the LCM of two numbers, multiply the two numbers together. For more than two, use the LCM of the first two, then multiply by the third, and so on.

Rules

• Addition:
  a/b + c/b = (a + c)/b
• Subtraction:
  a/b - c/b = (a - c)/b

Simplifying

• After adding or subtracting, always simplify by dividing the numerator and denominator by their greatest common factor (GCF).

Example

Simplify: 2/3 + 1/6

LCM of 3 and 6 is 6. 2/3 = 4/6 and 1/6 remains 1/6.

4/6 + 1/6 = 5/6

Important Note

You can only add or subtract rational expressions if they have the same denominator.