\(B = {{1 + {2 \over {x - 1}}} \over {1 + {{2x} \over {{x^2} + 1}}}}\)
\(\eqalign{& B = \left( {1 + {2 \over {x - 1}}} \right):\left( {1 + {{2x} \over {{x^2} + 1}}} \right) \cr & = \left( {{{x - 1} \over {x - 1}} + {2 \over {x - 1}}} \right):\left( {{{{x^2} + 1} \over {{x^2} + 1}} + {{2x} \over {{x^2} + 1}}} \right) \cr & = {{x - 1 + 2} \over {x - 1}}:{{{x^2} + 1 + 2x} \over {{x^2} + 1}} \cr & = {{x + 1} \over {x - 1}}.{{{x^2} + 1} \over {{{(x + 1)}^2}}} \cr & = {{{x^2} + 1} \over {\left( {x - 1} \right)\left( {x + 1} \right)}} \cr} \)
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