To solve this equation, we first need to find a common denominator for the fractions on the left side of the equation.

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

We can factor the denominator x^2-1 as (x+1)(x-1), which allows us to rewrite the equation as:

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

Now we can find a common denominator for the fractions on the left side:

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

Now we can combine the fractions:

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

Now combine the like terms:

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

Now cross multiply to eliminate the fractions:

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

Expand and simplify:

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

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

Rearrange the terms:

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

Combine like terms:

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

This is a fourth-degree polynomial equation. To solve it, you can try factoring, using the rational root theorem, or a numerical method like graphing or a calculator.