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Let T = {x|(x+5)/(x-7)-5=(4x-40)/(13-x)}...

Let `T = {x|(x+5)/(x-7)-5=(4x-40)/(13-x)}`. Is T an empty set ? Justify your answer.

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To determine whether the set \( T = \{ x \mid \frac{x+5}{x-7} - 5 = \frac{4x-40}{13-x} \} \) is empty or not, we need to solve the equation given in the set definition. ### Step-by-Step Solution: 1. **Start with the given equation:** \[ \frac{x+5}{x-7} - 5 = \frac{4x-40}{13-x} \] ...
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