Question 1122979
<pre>{{{y = (e^x + e^(-x))/(e^x - e^(-x))}}}

Multiply right side by {{{e^x/e^x}}}

{{{y = expr(e^x/e^x)((e^x + e^(-x))/(e^x - e^(-x)))}}}

Simplify:

{{{y = (e^(2x) + e^0)/(e^(2x) - e^0)}}}

Simplify:

{{{y = (e^(2x) + 1)/(e^(2x) - 1)}}}

Multiply both sides by {{{e^(2x)-1}}}

{{{y(e^(2x) - 1) = e^(2x) + 1}}}

Distribute on left:

{{{y*e^(2x) - y = e^(2x) + 1}}}

Get terms in {{{e^(2x)}}} on left side, others on right:

{{{y*e^(2x) -  e^(2x) = y + 1}}}

Factor out {{{e^(2x)}}} on the left side:

{{{e^(2x)(y-1) = y + 1}}}

Divide both sides by y-1

{{{e^(2x) = (y + 1)/(y-1)}}}
 
Take natural logs of both sides:

{{{ln(e^(2x)) = ln((y + 1)/(y-1))}}}

{{{2x*ln(e) = ln((y + 1)/(y-1))}}}

{{{2x(1) = ln((y + 1)/(y-1))}}}

{{{2x = ln((y + 1)/(y-1))}}}

Multiply both sides by {{{1/2}}}

{{{expr(1/2)2x = expr(1/2)ln((y + 1)/(y-1))}}}

{{{x = expr(1/2)ln((y + 1)/(y-1))}}}

Edwin</pre>