In throttling process, work done is zero.
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That means that no work is done.
No, unless both are zero. No work is done in a horizontal motion. mGh is work in a vertical direction.
Zero is not used as the divisor when dividing with the process of division.
In this case, V would be negative, and work w would be positive.
Dividing by zero is impossible and should never be done. My old math teacher used to have a Mathematical Ten Commandments and "You shall not divide by zero was one of them."