Ratio

$Let\quad the\quad numbers\quad be\quad m\quad and\quad n.\\ \\ \Rightarrow \quad x=\frac { m+n }{ m-n } \\ \Rightarrow \quad xm-xn=m+n\\ \Rightarrow \quad m(x-1)=n(x+1)\\ \Rightarrow \quad \frac { m }{ n } =\boxed { \frac { x+1 }{ x-1 } }$

$\dfrac{x}{1} = \dfrac{m+n}{m-n}$
Add on both sides of the equation, the denominators to the numerators, and subtract the numerators from denominators. We get $( x+1)/(1-x)=2m/-2n.......\implies \frac{m}{n} =\dfrac{x+1}{x-1}$

This is the Dividendo-Componendo Method of Ratios.