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