## Thursday, 24 January 2013

### Summary on Partial Fractions – Justin

PARTIAL FRACTIONS

Objective: To simplify algebraic fractions into two separate fractions, or a sum of a polynomial and a fraction.

Types of Fractions:
Not in partial form
Improper– Where the highest power of the unknown in the numerator is higher than that of the denominator. If the powers are the same, the numerator's coefficient of the power with the highest unknown would be higher than that of the denominator.

Proper – Where the highest power of the unknown in the numerator is less than that of the denominator. If both highest powers are equal, the coefficient of the numerator's unknown with the highest power is less than that of the denominator.

In Partial form
'Mixed Fraction' – If the fraction is improper, we must represent it as the sum of a polynomial and a fraction. Thus we have to first use long division, with the denominator as the divisor, to divide the numerator and obtain our polynomial/whole number.
The remainder would then have to be separated as well.

Partial Fraction – "Taking apart one algebraic fraction with a quadratic denominator into two separate fractions, often with a linear denominator."

How to represent fractions as partial fractions: