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CIE A Level Maths: Pure 3復(fù)習(xí)筆記1.3.3 Quadratic Denominators

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月19日 下午2:52

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

1-3-3-cie-fig1-we-solution-quad-den

1-3-3-cie-fig1-we-solution-quad-den_2

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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