Year 9: Addition and subtraction of rational expressions

This cheat sheet covers adding and subtracting rational expressions (fractions with variables).

Key concepts

• Rational expression: An expression that can be written as a fraction where the numerator and denominator are polynomials.
• Simplifying before combining: ALWAYS simplify fractions *before* adding or subtracting.

Rules

1. Common denominator

You MUST have a common denominator before adding or subtracting.

1. Find the least common multiple (LCM) of all denominators.
2. Multiply both numerator and denominator of each fraction by the LCM.

2. Adding rational expressions

Add the numerators and keep the common denominator.

Example: $(2/x)+(3/2x)=(4/2x)+(3/2x)=(4+3)/\left(2x\right)=7/2x$

3. Subtracting rational expressions

Similar to addition, but subtract the numerators.

Example: $(5/y)-(2/3y)=(15/3y)-(2/3y)=(15-2)/\left(3y\right)=13/3y$

4. Important notes

• You can only add or subtract fractions with the same denominator.
• Simplify your answer – make sure your numerator and denominator have no common factors.