Assume that the expression is f = uv/(u + v)
Multiply both sides by u + v to get:
f(u + v) = uv
Distribute...
fu + fv = uv
Then, subtract both sides by fu...
fu - fu + fv = uv - fu
fv = uv - fu
Subtract both sides by uv..
fv - uv = uv - uv - fu
fv - uv = -fu
Factor the left side expression:
v(f - u) = -fu
Divide both sides by f - u to get:
v = -fu/(f - u)
v = fu/-(f - u)
v = fu/(u - f)
I hope this helps!