`3/(x^4 + x)` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

Expert Answers

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Let's factorize the denominator,



Let `3/(x^4+x)=A/x+B/(x+1)+(Cx+D)/(x^2-x+1)`






equating the coefficients of the like terms,

`A+B+C=0`       - equation 1

`-B+C+D=0`    - equation 2

`B+D=0`              - equation 3


Plug the value of A in equation 1,




Substitute the above expression of C in equation 2,



`-2B+D=3`      - equation 4

Now solve equations 3 and 4 to get the solutions of B and D,

Subtract equation 3 from equation 4,




Plug the value of B in equation 3,



Plug the value of A and B in equation 1,






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