Show that ((coth x) +1) / ((coth x) -1) = e^2x

What do YOU think ?
While we're happy to HELP we wont do all the work for you.
Show us what you have done and where you are having problems..

Now you can figure it from this.
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CC8QFjAC&url=http%3A%2F%2Fwww.mathcentre.ac.uk%2Fresources% 2Fworkbooks%2Fmathcentre%2Fhyperbolicfunctions.pdf&ei=K1lEVPHXH4-QNrzSgfAP&usg=AFQjCNF6W_eQDHnr1n4g9xJsFIqc6kYFxA&sig2=lfgEzdu-2munFRPsFguH1A&bvm=bv.77648437,d.eXY

Simple matter of substituting the definitions of sinh(x) and cosh(x) for coth(x), and simplifying. If you're still having difficulty please post your work attempt and we'll help you along.