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### separation of variables / parameterizing equations in sage math

Hi,

I've sometimes run into the situation where sage math is unable to solve a system of equations that I then rearrange and am subsequently able to solve. The question is, Is sage able to do this re-arranging itself?

Example:

Given a contraint eq1, and eq2 for an op amp subtractor that mixes variables together

 eq1 = vout == (2*v1 - 3*v2) 
 eq2 = vout == (v1*(R4/(R3+R4))-(((v2-(v1*(R4/(R3+R4))))/R1)*R2)) 

can sage somehow rewrite this as an parameterized equation in terms of v1 and v2

 eq2 = vout == v1*( (R4/(R3+R4)+((R4/(R3+R4))/R1)*R2)) + v2*((-1/R1)*R2) 

Without my manual intervention?

I'd like to know if sage can detect that

2 == ( (R4/(R3+R4)+((R4/(R3+R4))/R1)*R2)) and -3 == ((-1/R1)*R2)

and solve those.

Can it also automatically detect if an equation can be safely separated in this way along some given variables??

Thanks to anyone who tries to answer this!