SOLUTION: Resolve the following improper fraction into partial fractions: (3x)/(x-3)^2

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Question 854555: Resolve the following improper fraction into partial fractions:
(3x)/(x-3)^2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%29%2F%28x-3%29%5E2

You must include a term with a denominator
which is a lower power of a denominator.
So since (x-3)² is to the 2nd power, you must
include a term with the lower power (x-3) in
the denominator.

3x%2F%28x-3%29%5E2%22%22=%22%22A%2F%28x-3%29%5E2%2BB%2F%28x-3%29

Notice also that even though (x-3)² is degree 2 if
multiplied out, we do not need "Ax+B" for its 
numerator because it is factored as the power of  
only a first degree binomial.

Clear of fractions:

3x%22%22=%22%22A%2BB%28x-3%29

3x%22%22=%22%22A%2BBx-3B

Since the sides must be identical, we can
equate the like terms on both sides:

3x%22%22=%22%22Bx

So B = 3

There are no constant terms on the left, so put 0

%220%22%22%22=%22%22A-3B

Substitute 3 for B

%220%22%22%22=%22%22A-3%283%29

%220%22%22%22=%22%22A-9

9%22%22=%22%22A

So

3x%2F%28x-3%29%5E2%22%22=%22%22A%2F%28x-3%29%5E2%2BB%2F%28x-3%29

becomes

3x%2F%28x-3%29%5E2%22%22=%22%229%2F%28x-3%29%5E2%2B3%2F%28x-3%29

Edwin