Hi Guys, I am trying to find the voltage across R3 using millmans theory. Any help would be great please see the attachment. I am stuck on the next step.
Just do the same things to both sides of the equation to get V into the numerator on just one side of the equation. You've built yourself a sufficiently complicated equation that you would be well advised to track your units carefully to catch mistakes you make. Also, in the stacked fraction you want to make it clear what is in the numerator and what is in the denominator because 1/(a/b) is NOT the same as (1/a)/b since division is not associative. The "S" is Siemens, which has units of 1/Ω or A/V and is a measure of conductance. So the first step is to get rid of the stacked fraction. Try multiplying the numerator and denominator (of just the stacked fraction) by the multiplicative inverse of the denominator.
Well, make your best attempt to do what I suggested and we'll get that corrected and take it from there.