<s>[INST] Why $\frac{x}{x+1}=\frac{1}{x^{-1}+1}$ I need some help understanding why $\frac{x}{x+1}=\frac{1}{x^{-1}+1}$.
I would be grateful if someone could explain. Be explicit.
Thank you!
 [/INST] $$\frac{x}{x+1} = \frac{x \cdot 1}{x \cdot (1+\frac{1}{x})}= \frac{x}{x} \cdot \frac{1}{1+\frac{1}{x}} = 1 \cdot \frac{1}{1+\frac{1}{x}} = \frac{1}{1+x^{-1}}$$
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