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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(x-1/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: x-1/x = (x-1)(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^2-1)/2x Could somebody please explain that jump from x-1/x to (x-1)(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 (x-1)(x+1)/x = (x² - 1)/x = x - 1/x. I take it you're aware that sinh(x) is defined as $\frac{e^x\,-\,e^{-x}}{\small2}$ and so sinh(ln(x)) = (x - 1/x)/2.

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