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Squared Linear Denominators (CIE A Level Maths: Pure 3)
Revision Note
Squared Linear Denominators
Partial fractions
- In partial fractions the common denominator is split into parts (factors)
- This is the reverse process to adding (or subtracting) fractions
- In harder questions there is a repeated factor, this is a squared linear factor
What are squared linear denominators?
- A linear factor is of the form (ax + b)
- It is possible b = 0 so a linear factor could be of the form ax (eg 4x)
- A squared linear factor is of the form (ax + b)2
- With b = 0 this would be of the form (ax)2 (x2 would be too!)
How do I find partial fractions with squared linear denominators?
STEP 1 Factorise the denominator (Sometimes the numerator can be factorised too)
STEP 2 Split the fraction into a sum with a squared linear denominator and any other single linear denominators
STEP 3 Multiply by the denominator to get rid of fractions
STEP 4 Substitute values of x to find A, B, etc (or use comparing coefficients)
STEP 5 Write the original as partial fractions
Worked example
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