Splitting into two fractions
Practice Flashcards
Flip to reveal answersHow do you split p(x)/[(x − a)(x − b)] (two different linear factors)?
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All 8 Flashcards — Splitting into two fractions
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Question
How do you split p(x)/[(x − a)(x − b)] (two different linear factors)?
Answer
Write it as A/(x − a) + B/(x − b), then find A and B.
Question
What is the cover-up method?
Answer
Clear the fractions, then substitute the x that makes one bracket zero — it deletes a term and leaves a single unknown.
Question
To find A (the numerator over (x − a)), which x do you substitute?
Answer
x = a — the root of its own bracket — which zeroes the OTHER term and isolates A.
Question
First step in any partial-fractions question?
Answer
Multiply both sides by the whole denominator to clear the fractions.
Question
Split (5x − 1)/[(x + 1)(x − 2)].
Answer
2/(x + 1) + 3/(x − 2).
Question
Split (x + 7)/[(x − 1)(x + 3)].
Answer
2/(x − 1) − 1/(x + 3).
Question
When can you use the two-fraction split?
Answer
When the bottom is two DIFFERENT linear factors, e.g. (x − 1)(x + 3).
Question
How do you check your A and B?
Answer
Add the two fractions back over a common denominator — you should recover the original fraction.
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Full study notes for Splitting into two fractions
Topic 1.11 hub
Partial fractions (HL only)
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