Inverting an equation with variables?

Question

1/s'=(1/f)-(1-s)

what would s' be.

i thought you would just have to invert each one and get s'=f-s but that is not the case.

spherical mirror equation

Answer 1

aka the lens formula, I think you mean 1/s'=1/f-1/s where, unless there are parenthesis to tell you what to do first, division is done before subtraction. Your answer violates the rules of algebra. To invert both sides you get:
s'=1/(1/f-1/s) which is a compound fraction. To make a simple fraction, multiply by 1=fs/(fs). You then get:
s'=fs/(s-f)

Answer 2

s' = 1/((1/f)-(1-s))

You can't split the 1/f and 1-s bits. There's not much else you can do to simplify it, but it could also be written

s' = 1/(1/f-1+s)