Algebraic fractions · Year 12
In Year 12 you learn: adding and subtracting 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.
- 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
Example 1
Simplify (x² − 9)/(x² + 5x + 6).
Answer: (x − 3)/(x + 2)
Example 2
Write 3/(x + 2) + 2/(x − 1) as a single fraction.
Answer: (5x + 1)/((x + 2)(x − 1))