First, we need to find a common denominator for the two fractions on the left side:

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

The common denominator will be (x-1)(x+1):

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

Now, we can expand the numerators:

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

Combine like terms:

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

Now, we can set the numerator equal to the denominator:

2x^3 - 6x + 4 = x^2 - 1

Rearrange the equation:

2x^3 - x^2 - 6x + 4 + 1 = 0

2x^3 - x^2 - 6x + 5 = 0

Therefore, the final solution is 2x^3 - x^2 - 6x + 5 = 0