Question

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.

x-2
________
x^2+11x+28

Answer 1

A/(x+7) +B/(x+4)

Explanation:

The denominators of the partial fraction expansion are the factors of the denominator of the rational function.

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Here, the rational function's denominator can be factored as ...

x² +11x +28 = (x +7)(x +4)

Then the form of the decomposition is ...

`(x-2)/(x^2+11x+28)=\boxed{(A)/(x+7)+(B)/(x+4)}`

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Additional comment

Here, A=3. B=-2.

If the factors of the denominator have multiplicity greater than 1, then there is a fraction with each power of that factor up to the multiplicity. For example, if there is a factor (x+4)³, then the decomposition would include fractions A/(x+4) +B/(x+4)² +C/(x+4)³.