Looks good to me. Probably a good idea not to mix upper-case and lower-case interchangeably throughout your derivations, though. It's clearer if you're consistent that way.
D = 1/ e - f , solve for F
is the work and answer
Multiply each side by e - f then you would have
d(e-f) = 1
Then
Divide by D
e-f = 1/d
Then Subtract e
-f = 1/d - e
Then multiply each side by -1
f = (-1/d) + e
Is this the answer?