Hyperbolic Graph Problem

May 2010
36
0
Hi,
please find attached the problem and the short and sweet Answer.
I can't understand the last step of the answer.
 

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Jan 2008
588
242
Hi,
please find attached the problem and the short and sweet Answer.
I can't understand the last step of the answer.
\(\displaystyle
-2e^k + 4e^{-k} = -2
\)

Moving everything to the left

\(\displaystyle
-2e^k + 2 + 4e^{-k} = 0
\)

Factorising \(\displaystyle -2e^{-k} \)

\(\displaystyle
-2e^{-k}(e^{2k} - e^k -2) = 0
\)

Divide both sides by \(\displaystyle -2e^{-k}\)

\(\displaystyle
e^{2k} - e^k -2 = 0
\)
 
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May 2010
36
0
tnx a lot so simple.. yet so much to assimilate :)

thanks again

Brandon