(3x-1/6x-3)-(1/1-4x2)=(x/2x+1)

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To simplify the equation, we need to first find a common denominator for each fraction:

(3x - 1)/(6x - 3) - 1/(1 - 4x^2) = x/(2x + 1)

Common denominators are:
6x - 3 = 3(2x - 1)
1 - 4x^2 = (1 - 2x)(1 + 2x)
2x + 1 = 1(2x + 1)

Now we rewrite the equation with the common denominators:

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

(3x + 6x^2 - 3)/(6x - 3) - (1 + 2x - 2x - 4x^2)/(1 - 4x^2) = x/(2x + 1)

(6x^2 + 3x - 3)/(6x - 3) - (1 - 4x^2)/(1 - 4x^2) = x/(2x + 1)

Now we can simplify the equation further:

(6x^2 + 3x - 3)/(6x - 3) - 1 = x/(2x + 1)

(6x^2 + 3x - 3 - 6x + 3)/(6x - 3) = x/(2x + 1)

(6x^2 + 3x - 3 - 6x + 3)/(6x - 3) = x/(2x + 1)

(6x^2 + 3x - 6x)/(6x - 3) = x/(2x + 1)

(6x^2 - 3x)/(6x - 3) = x/(2x + 1)

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

3x/3 = x/(2x + 1)

x = x/(2x + 1)

Therefore, the equation simplifies to x = x/(2x + 1), which is a true statement for all values of x.