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Flip to reveal answersWhat if the denominator is given as a quadratic, not two brackets?
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All 8 Flashcards — Getting it ready first
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Question
What if the denominator is given as a quadratic, not two brackets?
Answer
Factorise it first into (x − a)(x − b), then split as usual.
Question
When is a fraction 'top-heavy' (improper)?
Answer
When the top's highest power is as big as (or bigger than) the bottom's. You must divide first.
Question
How do you handle a top-heavy fraction?
Answer
Divide to peel off a whole part, leaving a proper fraction; then split the proper part into partial fractions.
Question
Split x²/[(x − 1)(x + 1)].
Answer
1 + (1/2)/(x − 1) − (1/2)/(x + 1) — divide first since x² = (x² − 1) + 1.
Question
Factorise x² + x − 6.
Answer
(x + 3)(x − 2).
Question
Factorise x² − 4 to split a fraction over it.
Answer
(x − 2)(x + 2) — difference of two squares.
Question
Besides cover-up, how else can you find A and B?
Answer
Equate coefficients: expand the right side and match the x-terms and the constant terms, then solve.
Question
Can you split (x² + 1)/(x² − 1) straight away?
Answer
No — same degree top and bottom (top-heavy). Divide first: it's 1 + 2/(x² − 1).
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Full study notes for Getting it ready first
Topic 1.11 hub
Partial fractions (HL only)
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