F=uv/u+v

make v the subject of the equation showing your working f=uv/u+v

make v the subject of the equation showing your working

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!