Hi, I thought I could do this last question in my exercise book but I have gone wrong somewhere. Could someone show me where please?

$\displaystyle f=\frac{uv}{u+v}$

$\displaystyle f(u+v)=uv$

$\displaystyle fu+fv=uv$

$\displaystyle fv=uv-fu$

$\displaystyle \frac{fv}{v-f}=u-u$