(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the partial fractions of 1/((3x)(5-x))

2. Relevant equations

3. The attempt at a solution

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

1=A(5-x)+B(3x)

If x=0

1=A(5-0)+B(3*0)=5A => A=1/5

If x=5

1=A(5-5)+B(3*5)=B15 => B=1/15

So

1/((3x)(5-x))=1/(15x)+1/(15*(5-x))

This is what I think it is supposed to be but the answer is slightly different where the third term is negative, 1/((3x)(5-x))=1/(15x)-1/(15*(5-x)). I don't see where the negative sign comes from. It has been a while since I've done partial fractions so I'd like to know if this method is correct.

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# Partial Fractions of 1/((3x)(5-x))

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