Algebraic Fractions

Study Notes

Algebraic fractions involve operations with fractions that contain algebraic expressions in the numerator or denominator. To add or subtract algebraic fractions, find the lowest common multiple of the denominators, adjust the fractions to have the same denominator, and then add or subtract the numerators. For multiplication and division, multiply or invert and multiply without needing a common denominator, and simplify by cancelling common factors.

Exam Tips

Key Definitions to Remember

• Algebraic Fraction — A fraction where the numerator or denominator contains algebraic expressions.
• Lowest Common Multiple (LCM) — The smallest multiple that is exactly divisible by each denominator.

Common Confusions

• Forgetting to find a common denominator for addition and subtraction.
• Incorrectly simplifying by cancelling terms across addition or subtraction.

Typical Exam Questions

• How do you add $\frac{1}{x} + \frac{1}{2y}$? Find the LCM, adjust denominators, and add numerators.
• How do you multiply $\frac{a}{b} \times \frac{c}{d}$? Multiply numerators and denominators, then simplify.
• How do you simplify $\frac{x^2 - 1}{x^2 + 2x + 1}$? Factorise and cancel common factors.

What Examiners Usually Test

• Ability to find and use the lowest common multiple for addition and subtraction.
• Correct multiplication and division of algebraic fractions.
• Simplifying fractions by cancelling common factors.