Advertisements (Quảng cáo)
Thực hiện các phép tính:
a)\(\left( {{x \over {x + 1}} + 1} \right):\left( {1 – {{3{x^2}} \over {1 – {x^2}}}} \right);\)
b)\(\left( {{x^2} – 1} \right)\left( {{1 \over {x – 1}} – {1 \over {x + 1}} – 1} \right)\)
Hướng dẫn làm bài:
a)\(\left( {{x \over {x + 1}} + 1} \right):\left( {1 – {{3{x^2}} \over {1 – {x^2}}}} \right) = {{x + 1 + 1} \over {x + 1}}:{{1 – {x^2} – 3{x^2}} \over {1 – {x^2}}}\)
\( = {{2x + 1} \over {x + 1}}:{{1 – 4{x^2}} \over {1 – {x^2}}} = {{2x + 1} \over {x + 1}}.{{1 – {x^2}} \over {1 – 4{x^2}}}\)
Advertisements (Quảng cáo)
\( = {{2x + 1} \over {x + 1}}.{{\left( {1 – x} \right)\left( {1 + x} \right)} \over {\left( {1 – 2x} \right)\left( {1 + 2x} \right)}} = {{1 – x} \over {1 – 2x}}\)
b)\(\left( {{x^2} – 1} \right)\left( {{1 \over {x – 1}} – {1 \over {x + 1}} – 1} \right) = \left( {{x^2} – 1} \right).\left[ {{{x + 1 – \left( {x – 1} \right) – \left( {x – 1} \right)\left( {x + 1} \right)} \over {\left( {x – 1} \right)\left( {x + 1} \right)}}} \right]\)
\( = \left( {{x^2} – 1} \right).{{x + 1 – x + 1 – {x^2} + 1} \over {\left( {x – 1} \right)\left( {x + 1} \right)}} = \left( {{x^2} – 1} \right).{{3 – {x^2}} \over {\left( {x – 1} \right)\left( {x + 1} \right)}}\)
\( = {{\left( {x – 1} \right)\left( {x + 1} \right)\left( {3 – {x^2}} \right)} \over {\left( {x – 1} \right)\left( {x + 1} \right)}} = 3 – {x^2}\)