# Algebra: fraction decomposition

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I have been working on a general appraoch to partial fractions. And I wanted a proof for why the normal way of doing partial fractions always gives a consistent equation system for the constants in the partial fraction. Question is illustrated with an example and explained more in detail in the document.

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This solution explores a method of fraction decomposition.

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Please see attached for computations.

Method of fraction decomposition

This process of taking a rational expression and decomposing it into simpler rational expressions that we can add or subtract to get the original rational expression is called partial fraction decomposition. Many integrals involving rational expressions can be done if we first do partial fractions on the integrand.

So, let's do a quick review of partial fractions. We'll start with a rational expression in the ...

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