Ive attached an example from a text book.

I dont understand why the 5 Ω resistor is taken out of the circuit?

 

Because the branch containing the 10 ohm resistor also includes the 5 ohm resistor in that branch,
they did not short the 10 ohm resistor, but the entire branch, containinmg both the 10 ohm and 5 ohm rersitors.

 

Thanks.
I now see the glaring mistake I made

 

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