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March 5th, 2014, 06:33 PM  #1 
Newbie Joined: Mar 2014 Posts: 1 Thanks: 0  Hyperbolic function question (simple)
Hi there, The question asks me to write the following as algebraic expressions of x. sinh(loge x) Now I've gotten it to the stage of: 1/2(x1/x) But I can't seem to get it further without thinking that I've mucked something up. Wolfram Alpha (https://www.wolframalpha.com/input/?i=% ... 9+simplify) says that I can turn: x1/x = (x1)(x+1)/x That would make the answer right but am I missing some sort of rule or something? I don't know how the above line can work? The answer is (x^21)/2x Could somebody please explain that jump from x1/x to (x1)(x+1)/x for me please? Thank you. 
March 5th, 2014, 09:44 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,757 Thanks: 2138 
(x  1)(x + 1) = x(x + 1)  1(x + 1) = x² + x  x  1 = x²  1, so (x1)(x+1)/x = (x²  1)/x = x  1/x. I take it you're aware that sinh(x) is defined as and so sinh(ln(x)) = (x  1/x)/2. 

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