Question

F = uv/u + v make u the subject

Answer 1

I'm assuming that you mean

$\dfrac{uv}{u+v}$

because if you meant

$\dfrac{uv}{u}+v$

then u would simplify and you couldn't make it the subject.

Under this assumption, we start with

$F=\dfrac{uv}{u+v}$

We multiply both sides by $u+v$

$F(u+v)=uv$

We expand the left hand side:

$Fu+Fv=uv$

We move all terms involving u to the left and all terms not involving u to the right:

$Fu-uv=-Fv$

We factor u on the left hand side:

$u(F-v)=-Fv$

We divide both sides by $F-v$

$u=\dfrac{-Fv}{F-v}$