`(3x)/(1+x-2x^2)=(1-2x)/(x-1)` Solve the equation.Thanks!

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The equation `(3x)/(1+x-2x^2)=(1-2x)/(x-1)` has to be solved.

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

=> `(3x)/(1+2x-x-2x^2)=(1-2x)/(x-1)`

=> `(3x)/(1+2x-x(1 + 2x))=(1-2x)/(x-1)`

=> `(3x)/((1 - x)(1+2x))=(1-2x)/(x-1)`

=> `(-3x)/(1+2x)=(1-2x)`

=> `-3x = 1 - 4x^2`

=> `4x^2 - 3x - 1 = 0`

=> `4x^2 - 4x + x - 1 = 0`

=> `4x(x - 1) + 1(x - 1) = 0`

=> `(4x + 1)(x - 1) = 0`

=> x = `-1/4` and x = 1

In the original equation substituting x = 1 gives an in indeterminate value. This root can be ignored.

The solution of the equation is x = `-1/4`

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