## Thursday, 24 January 2013

### Partial Fractions Summary - Kaelan

Partial Fractions:

Definition: The parts/components of a fraction in proper form of a factorable denominator that when added equal to the original fraction

Methods of solving

Finding the partial fractions (decomposing) of a fraction is the reverse operation of adding its factors.

BUT FIRST

If the degree of numerator is higher than the denominator, take it literally and divide fraction by long division. Then decompose the remainder.

1) Factorise denominator and put equals sign

2) Write a separate fraction for each factor on the RHS as the denominator.
-The numerator is the degree n of the denominator -1
-eg. numerator for linear (x+1) is a constant A -> A/x+1. numerator for quadratic is linear Bx+C...

3) For repeating factors, (x+1)^6. write a separate fraction for  x+1 , (x+1)^2, (x+1)^3 ...

4) Cross multiply numerators on RHS and remove the denominators on both sides.

5) Either compare coefficients or substitute values of x to find the unknowns A,B,C...

6) Substitute / Rewrite partial fractions with the correct numerator