Solve the following system of equations to find the values of $x$, $y$ and $z$. $${\frac {xy}{x+y}}=\frac 1 2$$ $${\frac {yz} {y+z}} =\frac 1 3$$ $${\frac{xz}{x+z}} = \frac 1 7$$
Can you show how the first equation can be arranged to get $\dfrac 1 x + \dfrac 1 y =2$?