Simplify : (x+y)/(x-y) - (x-y)/(x+y) - 2xy/(x^2 - y^2)

Simplify : $\frac{x+y}{x-y} - \frac{x-y}{x+y} - \frac{2xy}{x^2 - y^2}$

तपाईं प्रतिभाशाली हुनुहुन्छ । यस्ता समस्या त कति समाधान गर्नु भयो कति, हाेइन र?
तपाईं अफुलाई गणितमा अब्बल बनाउन चहानुहुन्छ भने यस प्रश्नमा दिइएको समस्याकाे समाधान गरेर देखाउनुहाेस् ।
If you want to be a genius in Mathematics, solve the followint problem.
Genius can solve any mathematical problem.
Mathematics Injection
$\large \textbf{Simplify:}$

Simplify : $\frac{x+y}{x-y} - \frac{x-y}{x+y} - \frac{2xy}{x^2 - y^2}$

Here,

$\frac{x+y}{x-y} - \frac{x-y}{x+y} - \frac{2xy}{x^2 - y^2}$

= $\frac{(x+y)^2 - {(x-y)^2}}{(x-y)(x+y)}- \frac{2xy}{x^2 - y^2} $

= $\frac{x^2 +2xy + y^2 - (x^2 - 2xy + y^2)}{x^2 - y^2}- \frac{2xy}{x^2 - y^2} $

= $\frac{x^2 +2xy + y^2 - x^2 + 2xy - y^2}{x^2 - y^2}- \frac{2xy}{x^2 - y^2} $

= $\frac{4xy}{x^2 - y^2}- \frac{2xy}{x^2 - y^2} $

= $\frac{4xy - 2xy}{x^2 - y^2} $

= $\frac{2xy}{x^2 - y^2}. $