Given "(x + y/z)" as input, how do I get the same expression in the form of "(xz+ y)/z". I need to make this conversion, so that I can discard  the denominator and use the numerator "xz +y" as a monomial in Groebner Basis.

Following set of equations will solve and give exact solutions for x1, x2, x5.

solve({
x1^2-x2^2-x3+x4=0,
(x2+1)^2-x5 = 0,
125+x1 - x2 = 0,
1+x3 - x4 = 0,
x8*x6+x7 - x8^2= 0,
x9*x6+x7 - x9^2-x3 = 0,
y2*x6+x7 - x5-y2^2 = 0,
y1*x6+x7+x5 - x5-y1^2-x4 = 0
},
[x1, x2, x3, x4, x5, x6, x7, x8, x9, y1, y2]);

One can solve simultaneous equations if there are sufficient number of unique equations. If I do not have sufficient number of equations, I would like to generate a response that prints what is missing. How do I accomplish that? Any ideas? Thanks a lot in advance.

Trivial linear equation sample: 2x + 3y=0, y=2 - z. Solve x, y, z.