`(x + 2)/(x(x^2 - 9))` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

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Now let `(x+2)/(x(x^2-9))=A/x+B/(x+3)+C/(x-3)`






equating the coefficients of the like terms,




Solve the above three equations to get the values of A,B and C,


Bach substitute the value of A in the first equation,



From the above equation ,express C in terms of B


Substitute the expression of C in the second equation,






Now plug the value of B in the expression of C,






Now let's check the result,









Hence it is verified.

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