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

Linear Denominators

What are partial fractions?

• This is the reverse process to adding (or subtracting) fractions

• When adding fractions a common denominator is required

• In partial fractions the common denominator is split into parts (factors)

• Partial fractions are used in binomial expansions (see Multiple GBEs) and integration (see Integration by Parts)

What are linear denominators?

• A linear factor is of the form (ax + b)

• A non-linear denominator may be written as the product of linear factors

• If the denominator can be factorised

How do I find partial fractions?

STEP 1        Factorise the polynomial in the denominator

(Sometimes the numerator can be factorised too)

STEP 2        Split the fraction into a sum with 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

(An alternative method is comparing coefficients)

STEP 5        Write the original as partial fractions

Comparing coefficients

• The quantity of each term must be equal on both sides

• “The number of x² on the LHS” = “The number of x² on the RHS”

• “The number of …” is called the coefficient of x²