Question

How to simplify (x-1)[-x-2lnabs(x-1)+(x+1)lnabs(x-1)]?

Answer 1

\[(x-1)[-x-2\ln \left| x-1 \right|+(x+1)\ln \left| x-1 \right|]\]

Answer 2

begin by taking \(\ln \left| x-1 \right|\) as a common factor:
\[(x-1)\left[ -x-2\ln \left| x-1 \right|+(x-1)\ln \left| x-1 \right| \right]\]
\[(x-1)\left[ -x+\ln \left| x-1 \right|(x+1-2) \right]\]
\[(x-1)\left[ -x+\ln \left| x-1 \right|(x-1) \right]\]

Answer 3

Thanks.