So I'm going to take moments about here, and

I'll assume that counterclockwise direction is positive.

And again, it doesn't matter which direction you assume here.

Summing the cuts about that point equal to zero, for equilibrium.

We have a known moment here, M.

We have the moment of P, and the moment of Ra.

And solving that, we find that the moment there, the bending moment,

is equal to PL over 8, minus M zero, over 2.

Next I'll make a cut just to the right of the mid point.

So, now I'm going to make my cut right here.

Just to the right of that applied moment.

And here is my new free body diagram.

Which is similar to the first one.

Except now we have this additional concentrated moment.

M0 applied.

So I do the same analysis.

First of all, sum the forces in the vertical direction.

And that leads to exactly the same equation, and

the same result for the shear force V.