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This seemed easy...at first

Can someone please help me with a problem?

I'm studying op-amps and can't quite figure this one out. It's analyzing a noninverting op-amp circuit to find the gain. You shouldn't need any electronic knowledge to figure this out - it's just algebra.

Here goes:

V_{in} = V_{out}R_{1}/(R_{1} + R_{2})

gain = V_{out}/V_{in} = 1 + R_{2}/R_{1}

I cannot figure out, no matter what I try, how to get from the first equation to the second. Can someone please give me a step-by-step solution?

Attached is a copy of the entire text for context.

Thanks!

Attachment 29776

Re: This seemed easy...at first

$\displaystyle \frac{V_{\text{out}}}{V_{\text{in}}} =\frac{V_{\text{out}}}{V_{\text{out}}R_1/(R_1+R_2)} =\frac{1}{R_1/(R_1+R_2)} =\frac{R_1+R_2}{R_1} =\frac{R_1}{R_1}+\frac{R_2}{R_1}=1+\frac{R_2}{R_1}$