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