CIE A Level Maths: Pure 3復(fù)習(xí)筆記1.3.3 Quadratic Denominators
Quadratic Denominators
What is meant by partial fractions with quadratic denominators?
How do I find partial fractions involving quadratic denominators?
- ?STEP 1??????????Factorise?the denominator as far as possible (if not already done so)
-
- Sometimes the numerator can be factorised too
- STEP 2??????????Split?the fraction into a?sum?with
- the?linear?denominator?having an (unknown)?constant?numerator
- the?quadratic?denominator?having an (unknown)?linear?numerator
- STEP 3????????? Multiply through by the denominator to eliminate fractions
Worked Example
Exam Tip
- You can check your final answer by?substituting?a value of?x?in to both the left and right-hand sides and seeing if they’re equal
- Choose a small value of?x??to keep things simple but not a value that would make a denominator zero
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