Question 61
Let $x$ and $y$ be distinct real numbers such that $2xy + 1 \neq 0$, and let
$$
A = \frac{6x^2y^2 + xy - 1}{2xy + 1} \quad \text{and} \quad B = \frac{x(x^2 - 1) - y(y^2 - 1)}{x - y}.
$$
Determine which number is larger, $A$ or $B$.
$$
A = \frac{6x^2y^2 + xy - 1}{2xy + 1} \quad \text{and} \quad B = \frac{x(x^2 - 1) - y(y^2 - 1)}{x - y}.
$$
Determine which number is larger, $A$ or $B$.