Express the following as partial fractions: a.) `(2x+1)/((x-1)^2)` ` ` b.)`(3)/((x+1)(x+2)(x+3))`  

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Since the denominator of the fraction is a repeated linear factor `(ax+b)^n` , its partial fraction decomposition is in the form:

`A_1/(ax+b) +A_2/(ax+b)^2+....+A_n/(ax+b)^n`



To determine the values of of A1 and A2, simplify the equation by multiplying both sides by the LCD of the three fractions.


`2x+1=A_1(x-1)+A_2`       (Let this be EQ1.)

Then, assign a value to x, such that A1 will be eliminated. And only A2 remains in the equation.

To do so, let x=1.




Now that value of A2 is known, plug-in this to EQ1.





Then, assign another value to x.

Let it be x=0.





Hence,  ` (2x+1)/(x-1)^2=2/(x-1)+3/(x-1)^2` .

(For the second problem, kindly post it as a separate question in Homework Help.)

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