# How do I find #A# and #B# in the partial fraction decomposition #91x+269=A(x+4)^2+B(x+4)#?

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I know how to do PFDs when there are two factors that are different, but how can I do this when there are two factors that are the same? If I set #x=-4# then I remove both terms, and then I have nothing left to solve for.

I know how to do PFDs when there are two factors that are different, but how can I do this when there are two factors that are the same? If I set

##### 1 Answer

#### Explanation:

If you take the original question:

and you apply long division to it you do indeed get:

However, once you clear the denominator by multiplying everything by

you get:

and to solve for A:

Thus, the partial fraction decomposition of

is