Year 10: Addition and subtraction of rational expressions

This cheat sheet covers the addition and subtraction of rational expressions (fractions with polynomials) in Algebra.

Key Concepts

• Common Denominator: The most crucial step! You MUST find a common denominator (LCD) for all the fractions. This is usually the least common multiple (LCM) of the denominators.
• Simplifying: After finding the LCD, add or subtract the numerators and then simplify the resulting rational expression.

Steps

1. Find the LCD: Calculate the LCM of all denominators.
2. Create Equivalent Fractions: Rewrite each fraction with the LCD as its denominator.
3. Add/Subtract Numerators: Add or subtract the numerators of the equivalent fractions.
4. Simplify: Factor the numerator and denominator and cancel out any common factors. Ensure your final answer is in its simplest form.

Rules

• Adding: Add numerators, keep the denominator.
• Subtracting: Subtract numerators, keep the denominator.

Example

Example: (1/x + 2/x²) = ((1 * x) + (2 * 1)) / (x * x) = (x + 2) / x²

Remember: Always simplify your answer!