Solve (e^x + e^-x) ÷ e^x – e^-x= 2 Solve (e^x + e^-x) ÷ e^x – e^-x= 2
B baselramjet New member Joined Mar 22, 2007 Messages 34 Apr 5, 2007 #1 Solve (e^x + e^-x) ÷ e^x – e^-x= 2 Solve (e^x + e^-x) ÷ e^x – e^-x= 2
pka Elite Member Joined Jan 29, 2005 Messages 11,971 Apr 5, 2007 #2 \(\displaystyle \L\begin{array}{rcl} \frac{{e^x + e^{ - x} }}{{e^x - e^{ - x} }} & = & 2\quad ,x \not= 0 \\ e^x + e^{ - x} & = & 2e^x - 2e^{ - x} \\ e^x - 3e^{ - x} & = & 0 \\ e^{2x} & = & 3 \\ x & = & \ln \left( {\sqrt 3 } \right) \\ \end{array}\)
\(\displaystyle \L\begin{array}{rcl} \frac{{e^x + e^{ - x} }}{{e^x - e^{ - x} }} & = & 2\quad ,x \not= 0 \\ e^x + e^{ - x} & = & 2e^x - 2e^{ - x} \\ e^x - 3e^{ - x} & = & 0 \\ e^{2x} & = & 3 \\ x & = & \ln \left( {\sqrt 3 } \right) \\ \end{array}\)