If $\frac{1}{x} + \frac{1}{y} = 3$ and $\frac{1}{x} - \frac{1}{y} = -7$ what is the value of $x + y$? Express your answer as a common fraction.
I notice that both equations have fractions involving $x$ and $y$, so I wonder if I can eliminate one of them by adding or subtracting the equations. If I add the equations, I get $\frac{2}{x} = -4$, so $x = -\frac{1}{2}$. If I subtract the equations, I get $\frac{2}{y} = 10$, so $y = \frac{1}{5}$. Now I can find $x + y$ by plugging in the values I found. I get $x + y = -\frac{1}{2} + \frac{1}{5} = -\frac{5}{10} + \frac{2}{10} = -\frac{3}{10}$. 