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**Summary**

- Start with a Proper Rational Expressions (if not do divisionfirst)
- Factor the bottom into: linear factors.
- Write out a
**partial fraction**for each factor (and everyexponent of each) - Multiply the whole equation by the bottom.
- Solve for the coefficients by. substituting zeros of thebottom.
- Write out your answer!

Hereof, what is partial fraction method?

The **method** of **partial fractions** is a**technique** for decomposing functions. like Y(s) above so thatthe inverse transform can be determined in a.

**decompose**a

**fraction**simply means totake it apart. The most basic way to

**decompose**a

**fraction**is to break into unit

**fractions**, which iswhen the numerator (top number) is 1. We can see that 5/8 is thesame as the unit

**fraction**1/8 five times.

Considering this, how do you solve improper partial fractions?

1. Divide if **improper**: If N(x)/D(x) is an**improper fraction**, divide the denominator into the numeratorto obtain a polynomial plus a proper **fraction**. Examples:Write the form of the **partial fraction** decomposition of therational expression. Do not **solve** for theconstants.

**You**must split it into two **fractions** using the method of partial**fractions**. Let A/(x+2) + B/(x+1) = 1/(x+2)(x+1) and byadding the **fractions you can** solve for A = -1 , B = 1 .**You** then need only **integrate** using the rule for thederivative of ln x .