I Transforming an equation with logarithms

[Pnin]

I want to approximate the logarithm of the Binomial coefficient log (n!/ ((n - m)! m!) with the the Stirling approximation log x! ≈ x log x - x

I got

n log n - m log m - (n - m) log(n - m)

but I want

(n - m) log (n/(n - m)) + m log (n/m)

Can someone help how to transform the first equation into the latter?

 

[Gaussian97]

Try to add and subtract $m \log{n}$ in your first expresion

 

[Pnin]

thanks!