Hướng dẫn: Ta thực hiện phép tính ở trong ngoặc trước.

a)\(\left( {{x \over {x + 1}} + 1} \right):\left( {1 - {{3{x^2}} \over {1 - {x^2}}}} \right)\)

\( = {{x + 1 + 1} \over {x + 1}}:{{1 - {x^2} - 3{x^2}} \over {1 - {x^2}}}\)

\( = {{2x + 1} \over {x + 1}}:{{1 - 4{x^2}} \over {1 - {x^2}}}\)

\( = {{2x + 1} \over {x + 1}}.{{1 - {x^2}} \over {1 - 4{x^2}}}\)

\( = {{2x + 1} \over {x + 1}}.{{\left( {1 - x} \right)\left( {1 + x} \right)} \over {\left( {1 - 2x} \right)\left( {1 + 2x} \right)}}\)

\( = {{1 - x} \over {1 - 2x}}\)

b)\(\left( {{x^2} - 1} \right)\left( {{1 \over {x - 1}} - {1 \over {x + 1}} - 1} \right)\)

\(= \left( {{x^2} - 1} \right).\left[ {{{x + 1 - \left( {x - 1} \right) - \left( {x - 1} \right)\left( {x + 1} \right)} \over {\left( {x - 1} \right)\left( {x + 1} \right)}}} \right]\)

\( = \left( {{x^2} - 1} \right).{{x + 1 - x + 1 - {x^2} + 1} \over {\left( {x - 1} \right)\left( {x + 1} \right)}}\)

\(= \left( {{x^2} - 1} \right).{{3 - {x^2}} \over {\left( {x - 1} \right)\left( {x + 1} \right)}}\)

\( = {{\left( {x - 1} \right)\left( {x + 1} \right)\left( {3 - {x^2}} \right)} \over {\left( {x - 1} \right)\left( {x + 1} \right)}}\)

\(= 3 - {x^2}\)