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I understand the voltage input at Rb gives the first two additions of the equations. But why is this subtracted from R3 and R4?

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The equation is correct, although the unsimplified form would be clearer. The first stage sums in the inverting input, which means that those terms should be negative when summed in the second stage. And then it inverts in the second stage.

-(-(a + b) + c + d) = a + b - c - d

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