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March 5th, 2014, 06:33 PM   #1
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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.
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March 5th, 2014, 09:44 PM   #2
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(x - 1)(x + 1) = x(x + 1) - 1(x + 1) = x + x - x - 1 = x - 1, so (x-1)(x+1)/x = (x - 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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