baselramjet
New member
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- Mar 22, 2007
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Solve (e^x + e^-x) ÷ e^x – e^-x= 2
Solve (e^x + e^-x) ÷ e^x – e^-x= 2
Solve (e^x + e^-x) ÷ e^x – e^-x= 2
Solve (e^x + e^-x) ÷ e^x – e^-x= 2
- Thread starter baselramjet
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pka
Elite Member
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- Jan 29, 2005
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- 11,971
\(\displaystyle \L\begin{array}{rcl}
\frac{{e^x + e^{ - x} }}{{e^x - e^{ - x} }} & = & 2\quad ,x \not= 0 \\
e^x + e^{ - x} & = & 2e^x - 2e^{ - x} \\
e^x - 3e^{ - x} & = & 0 \\
e^{2x} & = & 3 \\
x & = & \ln \left( {\sqrt 3 } \right) \\
\end{array}\)
\frac{{e^x + e^{ - x} }}{{e^x - e^{ - x} }} & = & 2\quad ,x \not= 0 \\
e^x + e^{ - x} & = & 2e^x - 2e^{ - x} \\
e^x - 3e^{ - x} & = & 0 \\
e^{2x} & = & 3 \\
x & = & \ln \left( {\sqrt 3 } \right) \\
\end{array}\)