Image formation by compound microscope at the least distance of distinct vision:

Expression for magnification:
For objective,
Magnification $={\mathit{m}}_{\mathit{o}}=\frac{\mathit{P}\prime \mathit{Q}\prime }{\mathit{P}\mathit{Q}}=\frac{-\mathit{v}}{\mathit{u}}$
When the image is formed at the least distance of distinct vision, then
Magnification $={\mathit{m}}_{\mathit{e}}=1+\frac{\mathit{D}}{{\mathit{f}}_{\mathit{e}}}$
So, final magnification $=\mathit{m}={\mathit{m}}_{\mathit{e}}=\frac{\mathit{v}}{\mathit{u}}\left(1+\frac{\mathit{D}}{{\mathit{f}}_{\mathit{e}}}\right)$