Partial Fractions with Squared Linear Denominators (AQA A Level Maths): Revision Note

Partial fractions with squared linear denominators

What are partial fractions with squared linear denominators?

• 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

• 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