MHB Simplifying an expression with exponents

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SUMMARY

The expression $$\frac {1} { e^x + \frac {1} {e^x}}$$ simplifies to $$\frac {e^x} { e^{2x} + 1}$$ through the application of algebraic manipulation. By multiplying the original expression by $$1=\frac{e^x}{e^x}$$, the simplification process becomes clear. This method effectively eliminates the complex fraction and results in a more manageable form.

PREREQUISITES
  • Understanding of basic algebraic manipulation
  • Familiarity with exponential functions
  • Knowledge of simplifying fractions
  • Ability to apply the concept of multiplying by one in algebra
NEXT STEPS
  • Study the properties of exponents in algebra
  • Learn techniques for simplifying complex fractions
  • Explore algebraic identities involving exponential functions
  • Practice problems involving the manipulation of expressions with exponents
USEFUL FOR

Students studying algebra, educators teaching exponential functions, and anyone seeking to improve their skills in simplifying mathematical expressions.

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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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