Partial Fractions
- Created by: eleanor
- Created on: 17-04-15 12:25
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- Partial Fractions
- Linear Fractions
- each factor becomes a denominator of a fraction- you need to then find A and B
- 1. cross multiply to find a single fraction
- 2. the denominators are the same so can be ignored
- 3. compare the numerators: 14x = A(x+3) + B(2x+1)
- 4. then use substitution to find A by eliminating B.
- if A or B are a fraction bring down the denominator to the bottom
- if there are 3 linear factors you solve in the same way.
- just be careful that each numerator must multiplied by the denominator of both of the other fractions
- a Repeated Linear Factor
- the repeated factor appears once as a linear denominator and once as a quadratic denominator
- 1. cross multiply as before but because there is an extra factor you can cancel this from every term.
- 2. compare the numerators and then use substitution
- 3.to find one of the unknowns you have to equate the coefficients
- you can equate x or x^2
- Improper Fractions
- the degree of the polynomials is the highest power so if the degree of the numerator is equal to or higher than the degree of the denominator then the fraction is improper
- you must divide first by using polynomial division
- the answer becomes (whole part of answer) + remainder/divisor
- spilt the remaining fraction into partial fractions using the usual method
- look out for the difference of two squares because the denominator can be spilt into 2 linear factors
- Linear Fractions
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