$${\frac{l}{2u}+\frac{l}{v-u}-\frac{x}{v-u} = \frac{l}{2(v-u)} + \frac{x}{u} \quad\Rightarrow\quad \frac{l}{2}(\frac{1}{u}+\frac{1}{v-u})=x(\frac{1}{u}+\frac{1}{v-u})}$$