Get two brackets, then split: Often the bottom is handed to you as a quadratic, not as two brackets. Factorise it first into (x − a)(x − b), then split exactly as before.
IB-style question — factorise, then split
Express (3x + 5)/(x² + x − 6) in partial fractions.
Step by step
- Factorise the bottom into two linear brackets.
- Split and clear the fractions.
- x = 2 → only B.
- x = −3 → only A.
- Write the answer.
Final answer
(4/5)/(x + 3) + (11/5)/(x − 2).
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it free for 7 days:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Start your 7-day free trial Full access to Aimnova Pro · cancel anytime
Same degree top and bottom → divide: If the top's highest power is as big as the bottom's, the fraction is top-heavy. You can't split it yet — first divide to peel off a whole number part, leaving a proper fraction to split.
IB-style question — top-heavy fraction
Express x²/[(x − 1)(x + 1)] in partial fractions.
Step by step
- Top and bottom are both degree 2 → top-heavy. The bottom is x² − 1, and x² = (x² − 1) + 1, so peel off a 1.
- Now split the proper part 1/[(x − 1)(x + 1)].
- x = 1 → A; x = −1 → B.
- Put the whole part back.
Final answer
1 + (1/2)/(x − 1) − (1/2)/(x + 1).