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Determining Transfer Function from Block Diagram

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I'm doing my homework and need to find a transfer function W_eg (from input g to output e) using given block diagram.

The problem is that the output e disappeared.I made a step by step solution how I was doing it. Could someone look if I'm doing it right?

Here, the first image is the initial diagram, and the others are my solution.Initial diagram

simplification 1simplification 2


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