Good day to all the members. I am rather new to Mathematica and I apologise if this is a redundant question or if it has been answered elsewhere on this forum. (I searched but could not find it) While I have used the Solve function to solve some equations they have always been in the traditional form given by the help function.

Is it possible to solve 1 set of statistics in terms of another set, when they both depend on the same variables.

For example:

U1 = Y1/(Y1 + Y2 + Y3)

U2 = Y2/(Y1 + Y2 + Y3)

V1 = Y1/Y3

V2= Y2/Y3

Solve[{V1, V2}, {U1, U2}]

I know from doing the calculations by hand that the solution is

U1=V1/(1+V1+V2)

U2=V2/(1+V1+V2)

but I have too many of these equations to do them all by hand.

Thanks for any help