# What are the rules to make partial fractions?

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I've got four in my book but sometimes i don't get the answer by simply following the rule this happens especially with substitution method of Partial fractions of A and B.

I've got four in my book but sometimes i don't get the answer by simply following the rule this happens especially with substitution method of Partial fractions of A and B.

Be careful, it can be a little complicated

I'll go through a few examples since there are countless problems with their own solution.

We need to write it as a sum.

The next bit can't be written as a generalised formula, but you have to follow simple fraction addition to combine all the fractions into one.

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To decompose a rational function into partial fractions, follow these steps:

- Factor the denominator completely.
- Write the rational function as a sum of fractions, one for each distinct factor of the denominator.
- For each factor of the denominator, set up an equation where the numerator of the partial fraction is a polynomial of one degree less than the factor's degree.
- Solve the equations to find the numerators of the partial fractions.
- Combine the partial fractions into a single expression.

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