Question

Partial Fraction. I am confused at one step.

Answer 1

\[(x+5)/(x-3)^2 dx\]

Answer 2

My book shows they used \[\frac{ x+5 }{ (x-3)^2 } = \frac{ A }{ x-3 } + \frac{ B }{ (x-3)^2 }\] Why did they not just use (x-3) ? without the ^2 on B and the left side.

Answer 3

@Mertsj I don't know how to explain, please help him

Answer 4

Ya, I can understand this one being hard to explain. It's just something you can probably see if you see it.

Answer 5

Well solving it further kind of helps me see that after the fractions are eliminated I am able to solve for a letter of choice, in this case B. Wheres I think if they were all the same, then I wouldn't be able to solve correctly. I just don't fully understand the reasoning behind it. It's fine, but I do appreciate the thought :).

Answer 6

Think of it this way: If you have the fraction 11/24 , one of the factors could be 1/2, 1/4, 1/8 Since you don't know which one is a factor, you have to account for all the possibilities. It's the same thinking with the algebraic fraction that have repeated factors in the denominator.

Answer 7

Thank you! It helps to think of it like that.

Answer 8

yw