## shamil98 one year ago Solve algebraically. $\frac{ e^x + e^{-x} }{ e^x - e^{-x} } = 5$ I started out by multiply both sides by the bottom fraction and whatnot and took the natural logs of both sides and resulted in error.. haven't done math in months..

1. ganeshie8

let $$e^x=u$$, rearrange the equation and get a quadratic

2. triciaal

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3. shamil98

Yeah that's what i did originally ^

4. shamil98

@ganeshie8 i'll try that right now

5. dan815

ya thats good enuff too

6. dan815

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7. dan815

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8. shamil98

OH

9. shamil98

IM DUMB

10. triciaal

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11. shamil98

thanks guys forgot that e^-x = 1/e^x xD

12. ganeshie8

if you're not really interested in the numeric value, you could save all that algebra by simply saying $$\coth x = 5 \implies x = \coth^{-1}(5)$$

13. ganeshie8