Corrected the error and explanation of
1 )
2)
3 ) x real number :
1) $\displaystyle ln (\frac{x+1}{x-2})=ln |x+1|-ln |x-2|$
2) $\displaystyle \sqrt{(1-\sqrt2)^2}=\sqrt{2}-1$
3) $\displaystyle \frac{1}{x}>2 \implies 1>2x$ AND $\displaystyle 1>2x \implies \frac{1}{x}>2$ if and only if $\displaystyle x>0$.