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(x-1)/(2x+1)+(2x+1)/(x-1)=(5)/(2)...

(x-1)/(2x+1)+(2x+1)/(x-1)=(5)/(2)

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(3)/(x+1)-(2)/(x-1)=(5)/(x^(2)-1)

((2x-1)/((x-1)(2x+3))=(1)/(5(x-1))+(k)/(5(2x+3))rArr k=

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(1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=

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(x^((5)/(2))+2x^(-(1)/(2)))/(x^((5)/(2))-x^(-(1)/(2)))x5/2+2x-1/2 Differentiate 5/2-1/2 with respect to x .