Partial Fraction Decomposition

In summary, partial fraction decomposition is a mathematical method used to break down a rational function into simpler fractions. It is useful in solving integrals and differential equations, simplifying algebraic expressions, and finding roots of polynomial equations. The process involves identifying factors, setting up equations, solving for coefficients, and combining fractions. It is commonly used in calculus, engineering, physics, and other scientific fields.
  • #1
Disar
28
0
Hey eveyone,

trying to determine the partial fraction decomposition of:

(22x^2+60x+58)
(s+1)(x^2+4x+5)^2

I got values for my unknowns A, B, C, D,E are:
A=5
B=-1777/29
C=-6143/29
D=-570/29
E=840/29

If anyone out there can double check these for me.
 
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  • #2
A self check with partial fractions is fairly easy. Set up the two equations with the partially fractioned version on the right and the original on the left and simplify the right side. See if the numerator turns out to be the same.
 

FAQ: Partial Fraction Decomposition

What is partial fraction decomposition?

Partial fraction decomposition is a mathematical method that involves breaking down a rational function into simpler fractions. It is used to simplify complex expressions and make them easier to work with in mathematical calculations.

Why is partial fraction decomposition useful?

Partial fraction decomposition is useful because it allows us to solve integrals and differential equations that would otherwise be difficult or impossible to solve. It also helps in simplifying complex algebraic expressions and finding the roots of polynomial equations.

How do you perform partial fraction decomposition?

The process of partial fraction decomposition involves breaking down a rational function into a sum of simpler fractions. This is done by equating the original function to an unknown sum of fractions with specific denominators, and then solving for the unknown coefficients using algebraic methods.

What are the key steps in partial fraction decomposition?

The key steps in partial fraction decomposition are: identifying the factors of the denominator, setting up equations to determine the unknown coefficients, solving for the coefficients, and then combining the fractions to form the final solution.

What are some common applications of partial fraction decomposition?

Partial fraction decomposition is commonly used in calculus, specifically in solving integrals and differential equations. It is also used in engineering, physics, and other fields of science where complex mathematical expressions need to be simplified for easier analysis and computation.

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