$\left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right) \times \left( x-y-\left( x+y \right) \right)$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$\left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right) \times \left( x-y-x-y \right)$
Since two opposites add up to $0$, remove them from the expression$\left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right) \times \left( -y-y \right)$
Collect like terms$\left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right) \times \left( -2y \right)$
Multiplying a positive and a negative equals a negative: $\left( + \right) \times \left( - \right)=\left( - \right)$$-\left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right) \times 2y$
Use the commutative property to reorder the terms$-2y \times \left( \frac{ 1 }{ x }+\frac{ 1 }{ y } \right)$