MHB Simplifying an expression with exponents

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The expression $$\frac {1} { e^x + \frac {1} {e^x}}$$ simplifies to $$\frac {e^x} { e^{2x} + 1}$$ through the multiplication of the original expression by $$1=\frac{e^x}{e^x}$$. This technique allows for the elimination of the fraction in the denominator. Applying this multiplication results in a more manageable form that can be further simplified. Understanding the rules of exponents and fractions is crucial for achieving this simplification. The process demonstrates the importance of manipulating expressions for clearer results.
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I have this expression

$$\frac {1} { e^x + \frac {1} {e^x}}$$

and it simplifies to

$$\frac {e^x} { e^{2x} + 1}$$

And I'm not sure how to get this simplification or what rules to apply to get to this simplification.
 
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Multiply your original expression by:

$$1=\frac{e^x}{e^x}$$
 

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