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For real numbers $w$ and $z$, $$ \frac{\frac{1}{w}+\frac{1}{z}}{\frac{1}{w}-\frac{1}{z}}=2014 $$ What is $\frac{w+z}{w-z} ?$ 
Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations
Muliply both sides by $\left(\frac{1}{w}-\frac{1}{z}\right)$ to get $\frac{1}{w}+\frac{1}{z}=2014\left(\frac{1}{w}-\frac{1}{z}\right)$. Then, add $2014 \cdot \frac{1}{z}$ to both sides and subtract $\frac{1}{w}$ from both sides to get $2015 \cdot \frac{1}{z}=2013 \cdot \frac{1}{w}$. Then, we can plug in the most simple values for $z$ and $w(2015$ and 2013 , respectively), and find $\frac{2013+2015}{2013-2015}=\frac{2(2014)}{-2}=-2014$. 