The rational expression (x+1)/(3(x-2)²) can be decomposed into partial fractions by factoring out the coefficient 3 from the denominator. The correct decomposition is represented as (1/3) * (A/(x-2) + B/(x-2)²), where A and B are constants to be determined. The coefficient 3 is included in front of the entire expression rather than in each individual partial fraction, simplifying the process of solving for A and B.
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Jimmy25 said:Homework Statement
Decompose the rational expression into a sum of partial fractions:
(x+1)/(3(x-2)2)
I am familiar with the method of decomposing fractions into a sum of partials fractions (solving for A, B, C, etc.). What is confusing me is the coefficient 3 in the denominator. Do I have to include the 3 in the denominator of all the partial fractions or just one? why?