Two metallic plate of equal thickness and coefficient thermal conductivity K1 and K2 put together face to face. A common plate is constructed. What is equivalent K?

We know that,

The equivalent K =   $\frac{L1 + L2}{\frac{L1}{K1}}$

where L1 & L2 are plate1 & Plate2 thicknesses, K1 & K2 are coefficient thermal conductivity of plate1 & Plate2 respectively.

But here L1 = L2 = L (say)

Then K = L+L/(L/K1 + L/K2)  =   $\frac{2K1K2}{K1+K2}$