We finally finished the book for Pre-Calculas and we decided to look at old information that we decided to skip over. One of the few things that we did was Partial Fraction Decomposition. Partial Fraction Decomposition is when you take an answer that is completely answered and turn it back to what it looked like before.
like if the answer for a question was:
1/x+1 +2/x+3
it would go to
(3x+5)
(x+1)(x+3)
To do this there are about four steps to set it up
1. Divide if improper
2. Factor Denominator
3. Linear
4. Quadratic
Also how do you solve it.
1. Multiply by LCD
2. Group terms by powers of x
3. Equate coefficients
4. Solve the system of equations
Now there are 4 cases.
the first case is when the system is just a binomial : x+1 or x-1 or etc.
So below is one example of case 1
You first try to factor it and then you put it as A and B.
After that you then make it so you find it as a common denominator
Then you use A and B and group it together with x^2 and x and regular numbers. then solve the system of equations at the end.
The second case involves bx+c which is only used when there is a square or exponent inside the paranthesis. You solve the same way and you keep going.
The Third case is when there is a square on the outside. You make it so first there is the first without the square and the second one with a square. Then you continue on.
The last case deals with long division. You only do this when the exponent is bigger on the top than the bottom. THen you continue to solve all the way through.
That is how you use partial fraction decomposition
SEE YOU NEXT WEEK!!!
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