# How do you find the partial fraction decomposition of the rational function?

Here's an example of decomposing a rational function (followed by integration, which is one of the main reasons for partial fraction decomposition):

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To find the partial fraction decomposition of a rational function, follow these steps:

- Factor the denominator of the rational function completely.
- Write the partial fraction decomposition using undetermined coefficients.
- Equate the original rational function to the sum of the partial fractions.
- Multiply both sides by the denominator of the original rational function to clear the fractions.
- Solve for the undetermined coefficients by comparing the coefficients of like terms on both sides of the equation.
- If necessary, use algebraic manipulation to simplify the resulting equations and solve for the coefficients.
- Once you have found the coefficients, rewrite the original rational function as the sum of the partial fractions with the coefficients you found.
- If applicable, check your solution by verifying that the partial fraction decomposition indeed equals the original rational function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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