Solve for x: (x+1)/(x-1)=(2)/(2x-1)+(2)/(x-1) any help is greatly appreciated!(:

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The equation (x+1)/(x-1)=(2)/(2x-1)+(2)/(x-1) has to be solved for x.

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

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

=> (x+1)/(x-1) = (2x - 2 + 4x - 2)/((2x-1)(x - 1))

=> (x+1) = (6x - 4)/(2x-1)

=> (2x - 1)(x+1) = (6x...

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The equation (x+1)/(x-1)=(2)/(2x-1)+(2)/(x-1) has to be solved for x.

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

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

=> (x+1)/(x-1) = (2x - 2 + 4x - 2)/((2x-1)(x - 1))

=> (x+1) = (6x - 4)/(2x-1)

=> (2x - 1)(x+1) = (6x - 4)

=> 2x^2 + 2x - x - 1 = 6x - 4

=> 2x^2 - 5x + 3 = 0

=> 2x^2 - 2x - 3x + 3 = 0

=> 2x(x - 1) - 3(x - 1)= 0

=> (2x - 3)(x - 1) = 0

=> x = 3/2 and x = 1

x = 1 can be ignored as that makes both the sides indefinite.

The solution of the equation is x = 3/2

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