Algebraic fractions · Year 13

In Year 13 you learn: equations with algebraic fractions.

Algebraic fractions are fractions with letters in them, like (x + 2)/(x − 3). They follow exactly the same rules as number fractions: simplify by cancelling common factors, and add or subtract using a common denominator.

Key facts

• Only cancel factors (things multiplied), never terms that are added: (x + 3)/(x + 5) cannot be simplified.
• Factorise the top and bottom first, then cancel any common brackets.
• Add or subtract over a common denominator: a/x + b/y = (ay + bx)/(xy).
• Multiply tops together and bottoms together; to divide, multiply by the reciprocal of the second fraction.
• To solve an equation with fractions, multiply every term by the common denominator.
• A fraction cannot be worked out when its denominator is 0.

Worked examples

Other years

• Algebraic fractions · Year 11
• Algebraic fractions · Year 12