Lesson Summary(25/1/13) / Partial Fractions summary(Lee Kai En)

Terms

Proper Fraction - A fraction where the numerator < denominator 
Improper Fraction - A fraction where the numerator > denominator
Proper Algebraic Fraction - A fraction where the degree of the numerator < degree of the denominator
Improper Algebraic Fraction - A fraction where the degree of the numerator > degree of denominator

What is partial fraction?
Partial fraction is the breaking up of a fraction to find the original parts of the fraction which will add up to give the final simplified expression.

Methods of finding partial fractions
Method 1: Decomposition
E.G. 

Step 1: Factorise denominator first 
Step 2: Split the fraction up.

Step 3: Make it such that the denominators "disappear"

Methods of solving
Method 1: Comparing coeffs.
E.G.    3x+5 = (2A+B)x + (A-3B)
            2A+B = 3
            A-3B = 5
.......simultaneous equation.......

Method 2: Substitution
E.G      3x+5 ≡ A(2x+1)+B(x-3)
         if x = 3, A = 2
    *(A can be found much easily)
         if x = 

After finding the values of the unknown(such as A and B), substitute in the values into the fractions and express it as a partial fraction.
E.G.