Question
$$1+\frac{\frac{1}{x}}{1}-\frac{1}{x}-1 = 0$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 1+\frac{\frac{1}{x}}{1}-\frac{1}{x}-1 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot1+x \cdot \frac{\frac{1}{x}}{1}-x\cdot\frac{1}{x}-x\cdot1 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x+1-1-x &= 0&& \text{simplify left side} \\[1 em]x+1-1-x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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