Let the given reactions be: (i) $A + B \rightleftharpoons C + D$; Equilibrium constant = $K_1$ (ii) $E + F \rightleftharpoons G + H$; Equilibrium constant = $K_2$

Reversing reaction (i), we get: (iii) $C + D \rightleftharpoons A + B$; Equilibrium constant = $1/K_1$ .

Now, add reaction (ii) and reaction (iii): $(E + F) + (C + D) \rightleftharpoons (G + H) + (A + B)$ $C + D + E + F \rightleftharpoons A + B + G + H$

The equilibrium constant for a net reaction obtained by adding two reactions is the product of the equilibrium constants of the individual reactions . Therefore, the equilibrium constant for the new reaction is: $K = \left(\frac{1}{K_1}\right) \times K_2 = \frac{K_2}{K_1}$.