Decomposition of a rational expression

[Jimmy25]

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?

 

[Ratio Test =)]

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?

$$\frac{x+1}{3(x-2)^2}=\frac{1}{3} \left( \frac{A}{x-2} + \frac{B}{(x-2)^2} \right) = \frac{A}{3(x-2)} + \frac{B}{3(x-2)^2}$$