`x^3/((x + 2)^2(x - 2)^2)` Write the partial fraction decomposition of the rational expression.

Expert Answers

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Let `x^3/((x+2)^2(x-2)^2)=A/(x+2)+B/(x+2)^2+C/(x-2)+D/(x-2)^2`







equating the coefficients of the like terms,





Now we have to solve the above four equations to get the solutions of A,B,C and D.

Rewrite the third equation as,


substitute the expression of ( A+C) from the first equation in the above equation,






Express C in terms of A from first equation,


Substitute the expressions of C and D in the second equation,



`-4A+2B=-3` (equation 5)

Substitute the expressions of C and D in the fourth equation,





`4A+2B=1` (equation 6)

Solve equation 5 and 6 to get the solutions of A and B,

Add equation 5 and 6,





Plug the value of B in the equation 5,






Now plug the values of A and B in the expressions of C and D,







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