document.write( "Question 744143: Please help me solve this equation: simplify $\"+%282%2B+%28ae%5E4x-ae%5E-4x%29%2F%28e%5Ex-e%5E-x%29%28ae%5Ex%2Bae%5E-x%29%29%5E1%2F2+=+2+\"$ \n" ); document.write( "

Algebra.Com's Answer #453223 by KMST(5328) $\"\"$ $\"About$

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Take out common factor a.
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Simplify, cancelling a's.
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Recognize and use difference of squares special products $\"%28b%2Bc%29%28b-c%29=b%5E2-c%5E2\"$
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Factors $\"e%5E%282x%29-e%5E%28-2x%29\"$ in numerators and denominator cancel out.
\n" ); document.write( " $\"+%282%2B+e%5E%282x%29%2Be%5E%28-2x%29%29%5E%281%2F2%29+=+2+\"$ Recognize square of binomial $\"e%5Ex%2Be%5E%28-x%29\"$
\n" ); document.write( " $\"+%28%28e%5Ex%2Be%5E%28-x%29%29%5E2%29%5E%281%2F2%29+=+2+\"$
\n" ); document.write( " $\"+e%5Ex%2Be%5E%28-x%29+=+2+\"$ --> $\"x=0\"$ (It's the minimum of the function)
\n" ); document.write( "If you know about hyperbolic functions, you may write the last equation as
\n" ); document.write( " $\"2%2Acosh%28x%29=2\"$ <--> $\"cosh%28x%29=1\"$ \n" ); document.write( "

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