Partial fractions is a way of "breaking apart" fractions with polynomials in them.
Why do we want to do this?
Because the partial fractions are each simpler. This may be a very important step in solving the more complicated fraction.
Partial Fraction Decomposition
Step 1: Factorise the denominator
Step 2: Write one partial fraction for each of the factors
Step 3: Cross multiple so that there are no more fractions
Step 4: Find the constant
It only works for Proper Rational Expressions, where the degree of the top is less than the bottom.
The degree is the largest exponent the variable has.
Type of Fractions:
Proper: the degree of the top is less than the degree of the bottom.
Improper: the degree of the top is greater than, or equal to, the degree of the bottom.
If your expression is improper, then do Polynomial long division first. Obtain the proper fraction (e.g the remainder), then resolve the proper fraction into partial fraction.
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