Algebraic Fractions

Study Notes

Algebraic fractions involve expressions with variables in the numerator and/or denominator. They can be added, subtracted, multiplied, or divided using specific rules.

• Algebraic Fraction — a fraction where the numerator and/or the denominator contains algebraic expressions.
  Example: $\frac{x}{y}$
• Lowest Common Multiple (LCM) — the smallest multiple that is exactly divisible by each denominator.
  Example: The LCM of $x$ and $2y$ is $2xy$.
• Simplifying Algebraic Fractions — reducing the fraction to its simplest form by factoring and cancelling common terms.
  Example: $\frac{2x^2}{4x}$ simplifies to $\frac{x}{2}$.

Exam Tips

Key Definitions to Remember

• Algebraic Fraction: A fraction with variables in the numerator and/or denominator.
• Lowest Common Multiple (LCM): The smallest multiple common to each denominator.

Common Confusions

• Forgetting to find the LCM when adding or subtracting algebraic fractions.
• Incorrectly simplifying fractions by cancelling terms across addition or subtraction.

Typical Exam Questions

• How do you add $\frac{1}{x}$ and $\frac{1}{2y}$?
  Find the LCM, make denominators the same, then add numerators.
• Simplify $\frac{3x^2}{6x}$.
  Factor and cancel common terms to get $\frac{x}{2}$.
• What is the LCM of $x$ and $2y$?
  $2xy$.

What Examiners Usually Test

• Ability to find the LCM and adjust denominators for addition/subtraction.
• Simplifying algebraic fractions correctly by factoring and cancelling common terms.