Physics - Pulley Sample Problem

What is the acceleration of the following configuration?

Like with our atwood's machine example we solve this by looking at each mass individually. The forces acting on M are friction due to the table, opposing the tension T of the rope. The forces acting on m is the weight of m and the tension T of the rope. Now for atwood's situation we started with

m₁ g - T = m₁ a

T - m₂ g =  m₂ a

and arrived at

a = g(m₁ - m₂ )/(m₁ + m₂ )

For this situation, we can see that m1 can be substituted with M as we define positive acceleration as M going left and m going up, and negative acceleration as M to the right and m going down matching the convention of gravity's downward acceleration. The only difference is that instead of m₁ g being the force opposing T we have μMg which is the friction force due to the table. Making this substitution we arrive at

a = g(μM - m )/(M + m )