1. The problem asks which of the given equalities or inequalities about the function $$f(x)=\frac{2x}{x^2 + x} - \frac{2x}{x^2 - x}$$ is true.\n\n2. Calculate $$f(-x)$$ by substituting $$-x$$ into the function:\n$$f(-x) = \frac{2(-x)}{(-x)^2 + (-x)} - \frac{2(-x)}{(-x)^2 - (-x)} = \frac{-2x}{x^2 - x} - \frac{-2x}{x^2 + x} = -\frac{2x}{x^2 - x} + \frac{2x}{x^2 + x}$$\n\n3. Rewrite $$f(-x)$$ to compare with $$f(x)$$:\n$$f(-x) = \frac{2x}{x^2 + x} - \frac{2x}{x^2 - x}$$\n\n4. Notice that $$f(-x) = f(x)$$ as both expressions are the same.\n\n5. Therefore the statements:"A) $$f(-x) = f(x)$$" and "B) $$f(-x) - f(x) = 0$$" are both true, they are equivalent statements.\n\n6. Statement C) $$f(-x) \neq -f(x)$$ is also true because $$f(-x) = f(x)$$ not the negative of $$f(x)$$.\n\n7. Statement D) "none are true" is false because at least some statements are true.\n\nFinal conclusion: A), B), and C) are true statements for the function.