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September 2, 2014

September 2, 2014

Posted by **Brianna** on Friday, December 31, 2010 at 12:55am.

- calculus -
**drwls**, Friday, December 31, 2010 at 3:19amI think you mean partial fractions. That is what this method was called when I went to school. First factor the denominator.

(5x+1)/(x^2-x-12) = (5x+1)/[(x-4)(x+3)]

This can be written as

A/(x-4) + B/(x+3) where A and B are certain constants. Here is how you can solve for A and B.

Require that

(5x+1)/[(x-4)(x+3)] = A/(x-4) + B/(x+3)

= [A(x+3) +B(x-4)]/[(x-4)(x+3)]

= (A+B)x +3A-4B

This will be true if A+B = 5 and 3A-4B = 1

4A+4B = 20

Solve for A and B

3A+3B = 15

3A-4B = 1

7B = 14

B = 2 A = 3

So the answer is

3/(x-4) + 2/(x+3)

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