For a non inverting action, a simple way to obtain it is to keep the
feedback loop in place and connecting the terminal where the input used
to be connected, to ground, while feeding the input signal to the non
inverting input.
This makes the opamp create an output voltage so that the current
flowing through the feedback resistor network will be the necessary to
develop a voltage at the inverting input that is the same as the non
inverting input.
Since we know that the inputs draw virtually no current, then the
voltage at the inverting terminal will be defined by the voltage divider
created with by the feedback network.
Vinv = VoutR2 / (R1 + R2)
Since Vinv, the inverting input, is at the same potential as the non inverting input, then
Vin = VoutR2/(R1+R2)
The gain is the ratio of output voltage to input voltage
gain = Vout/Vin
A rewrite of the Vin equation gives you
Vin/Vout = R2/(R1+R2)
This las equation is the inverse of what we need, so lets get it straight
Vin = Vout R2/(R1+R2)
Vin (R1+R2) = Vout R2
(R1+R2) = R2 (Vout/Vin)
(R1+R2)/R2 = Vout/Vin
That's an equation for gain, which can be further simplified by separating the terms
(R1/R2) + (R2/R2) = Vout/Vin
(R1/R2) + 1 = Vout/Vin
As you can see, the gain is similar to the inverting amplifier, set by
the ratio of the feedback resistors. In this case however, the gain will
always be higher than 1. You can think of it as if the amplifier is
adding the amplified signal to the non inverting reference voltage,
which in fact is the same as the inverting, just that in this case the
reference is not ground (0v).
