MHB Can You Prove This Using Fraction Division?

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The discussion focuses on proving a mathematical concept using fraction division, specifically involving the division of the numerator and denominator by the exponential function $e^{1/x}$. Participants are encouraged to provide a detailed step-by-step process to demonstrate the proof. The hint suggests that manipulating the fraction in this way may simplify the problem. The request for clarity indicates a need for thorough explanations in mathematical proofs. Overall, the thread seeks to clarify the application of fraction division in this context.
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can someone prove this and show the process in detail? Many thanks :)
 
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Hint: divide top and bottom of that fraction by $e^{1/x}$.
 
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