2) \( \left(\frac{5 x+4 y}{5 x-4 y}-\frac{5 x-4 y}{5 x+4 y}\right):\left(\frac{5 x-4 y}{5 x+4 y}-\frac{5 x+4 y}{5 x-4 y}\right) \)

First, let’s simplify the expression step by step. The expression given is: \[ \frac{5 x + 4 y}{5 x - 4 y} - \frac{5 x - 4 y}{5 x + 4 y} \] We can combine the two fractions by finding a common denominator: \[ = \frac{(5 x + 4 y)^2 - (5 x - 4 y)^2}{(5 x - 4 y)(5 x + 4 y)} \] Expanding the squares, we have: \[ = \frac{(25x^2 + 40xy + 16y^2) - (25x^2 - 40xy + 16y^2)}{(5 x - 4 y)(5 x + 4 y)} \] This simplifies to: \[ = \frac{80xy}{(5 x - 4 y)(5 x + 4 y)} \] Now, let’s simplify the second part of the original expression: \[ \frac{5 x - 4 y}{5 x + 4 y} - \frac{5 x + 4 y}{5 x - 4 y} \] Following the same process: \[ = \frac{(5 x - 4 y)^2 - (5 x + 4 y)^2}{(5 x + 4 y)(5 x - 4 y)} \] Expanding, we obtain: \[ = \frac{(25x^2 - 40xy + 16y^2) - (25x^2 + 40xy + 16y^2)}{(5 x + 4 y)(5 x - 4 y)} \] This simplifies to: \[ = \frac{-80xy}{(5 x + 4 y)(5 x - 4 y)} \] Now, we combine the two simplified results: The overall expression now looks like: \[ \frac{\frac{80xy}{(5 x - 4 y)(5 x + 4 y)}}{\frac{-80xy}{(5 x + 4 y)(5 x - 4 y)}} \] Dividing the numerators by the denominators yields: \[ = \frac{80xy}{-80xy} = -1 \] Therefore, the final simplified expression is: \[ \boxed{-1} \]