Solve the exponential equation and approximate the result, correct to three decimal places   e^x+e^-x ------------- e^x-e^-x

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem does not provide an equation since it specifies the fraction only and the equal sign is missing. You need to solve the equation, hence, you should transform the given expression into an equation such that:

`(e^x + e^(-x))/(e^x -e^(-x)) = 0`

Notice that denominator cannot be zero, hence, you need to put the numerator equal to zero such that:

`e^x + e^(-x) = 0`

Using the negative power property yields:

`e^(-x) = 1/(e^x)`

`e^x + 1/(e^x) = 0`

Bringing the terms to a common denominator yields:

`e^x*e^x + 1 = 0 =gt e^(2x) = -1` , impossible

Notice that solving the equation `e^x + e^(-x) = 0`  yields to a contradiction, `e^(2x) = -1` , since the exponential function is larger than 0 for all values of x.

Hence, solving the equation `(e^x + e^(-x))/(e^x - e^(-x)) = 0` , yields that there are no solution to this equation.