# Transposition of Formula

#### Steve1992

Joined Apr 7, 2006
100
In context to an non-inverting op-amp (from text book)

Vin = Vo x Ri/Ri + Rf

Rearranging:

Vo = (1 + Rf/Ri) x Vin

I believe Ri is the common factor from the first equation, but I dont know how to get to the second equation.
If any one can give me the sequence of steps?

#### hgmjr

Joined Jan 28, 2005
9,029
In context to an non-inverting op-amp (from text book)

Vin = Vo x Ri/Ri + Rf
First, the equation you have shown should have parenthesis around the two terms in the denominator like below.
Vin = Vo x Ri/(Ri + Rf)

Start by multiplying both sides of the equal sign by (Ri + Rf).

Next, multiply both sides of the equal sign by Ri.

Then, you should have the expression

Vo = Vin*(Ri+Rf)/Ri

Next, expand the fraction to Vin*(Ri/Ri + RF/Ri)

Since Ri/Ri = 1 then you can substitute to get:

Vo = Vin*(1+(Rf/Ri))

Rearranging:

Vo = (1 + Rf/Ri) x Vin

I believe Ri is the common factor from the first equation, but I dont know how to get to the second equation.
If any one can give me the sequence of steps?