Consider the following equation:
This can be solved for Vout/Vin in the following way:
But what happens when I take the original equation and multiply by Rin+Rf on both sides to eliminate the denominator term as such:
I know intuitively that the answer is wrong and that you cannot simply multiply an equation of the form x/y+z/y=0 by y. How do you know when you can multiply both sides by a constant and when you cannot? It seems multiplying by a constant when one side of the equation equals zero is not allowed.
This can be solved for Vout/Vin in the following way:
But what happens when I take the original equation and multiply by Rin+Rf on both sides to eliminate the denominator term as such:
I know intuitively that the answer is wrong and that you cannot simply multiply an equation of the form x/y+z/y=0 by y. How do you know when you can multiply both sides by a constant and when you cannot? It seems multiplying by a constant when one side of the equation equals zero is not allowed.
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