Question

Answer 1

\(\frac{1}{\left|x-2\right|}>2\)

=>\(\frac{1}{\left|x-2\right|}-2>0\)

=>1-2|x-2|>0

=>2|x-2|<1

=>\(\left|x-2\right|<\frac12\)

=>\(-\frac12

=>\(\frac32

=>A=(3/2;5/2)

|x-1|<1

=>-1<x-1<1

=>0<x<2

=>B=(0;2)

A\(\cap\) B=(3/2;5/2)\(\cap\) (0;2)

=(3/2;2)

A\(\cup\) B=(3/2;5/2)\(\cup\) (0;2)

=(0;5/2)

A\B=(3/2;5/2)\(0;2)

=[2;5/2)

B\A=(0;2)\(3/2;5/2)

=(0;3/2]

(A\B)\(\cup\) (B\A)

=(0;3/2]\(\cup\) [2;5/2)