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December 18, 2014

December 18, 2014

Posted by **Austin** on Thursday, January 3, 2013 at 11:46pm.

In (x/x-1)+In(x+1/x)-In(x^2-1)

Please show work.

- math -
**Reiny**, Friday, January 4, 2013 at 12:11amYou MUST put brackets for the denominators to avoid ambiguity

I am sure you mean

ln ( x/(x+1) ) + ln( (x+1)/x ) - ln (x^2 - 1)

then

= lnx - ln(x+1) + (ln(x+1) - lnx - ln( (x+1)(x-1)

= lnx - ln(x+1) + ln(x+1) + lnx - ln(x+1) - ln(x-1)

= - 2ln(x+1)

or

ln [ (x/(x-1) ((x+1)/x) / ((x+1)x-1))

= ln (1/(x-1)^2)

= ln1 - ln(x-1)^2

= 0 - 2ln(x-1)

= -2ln(x-1)

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