3х/х^3-1 - 5/4х^2+4х+4 - 1/2(1-х)=0

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To solve this equation, we need to combine and simplify the terms:

3x/(x^3 - 1) - 5/(4x^2 + 4x + 4) - 1/2(1 - x) = 0

The denominator of the second term (4x^2 + 4x + 4) can be factored as 4(x^2 + x + 1).

Now we rewrite the equation with common denominators:

3x/(x^3 - 1) - 5/(4(x^2 + x + 1)) - 1/2(1 - x) = 0

Now multiply the second term by 4 to get a common denominator:

3x/(x^3 - 1) - 20/(4(x^2 + x + 1)) - 1/2(1 - x) = 0

Next, we simplify the equation:

3x/(x^3 - 1) - 20/(4x^2 + 4x + 4) - 1/2 + x/2 = 0

Multiplying through by (x^3 - 1) and (4x^2 + 4x + 4) to clear the fractions we have:

3x(4x^2 + 4x + 4) - 20(x^3 - 1) - 2(x^3 - 1) + x(x^3 - 1) = 0

Expanding and simplifying:

12x^3 + 12x^2 + 12x - 20x^3 + 20 - 2x^3 + 2 + x^4 - x + 0 = 0
-6x^3 + 12x^2 + 11x - 18 + x^4 = 0

Rearranging, we get:

x^4 - 6x^3 + 12x^2 + 11x - 18 = 0

Now, we can use numerical methods or factorization to solve for x.