If $\displaystyle \frac{1}{x+iy}+\frac{1}{u+iv}=1$; x,y,u,v being real quantities, express v in terms of x and y.

My Attempt: $\displaystyle \frac{(u+x)+i(y+v)}{(x+iy)(u+iv)}=1$

$\displaystyle (u+x)+i(y+v)=(xu-yv)+i(xv+yu)$

$\displaystyle (u+x)=(xu-yv)$

$\displaystyle (y+v)=(xv+yu)$

How to manipulate them further ?