Rút gọn phân thức:
a) \({{{x^4} – 1} \over {\left( {{x^2} – 1} \right)\left( {x + 2} \right)}}\)
b) \({{27{a^3} + {b^3}} \over {3ab + {b^2}}}\)
c) \({{{x^3} – {x^2} – x + 1} \over {{x^4} – 2{x^2} + 1}}.\)
Advertisements (Quảng cáo)
a) \({{{x^4} – 1} \over {\left( {{x^2} – 1} \right)\left( {x + 2} \right)}} = {{\left( {{x^2} – 1} \right)\left( {{x^2} + 1} \right)} \over {\left( {{x^2} – 1} \right)\left( {x + 2} \right)}} = {{{x^2} + 1} \over {x + 2}}.\)
b) \({{27{a^3} + {b^3}} \over {3ab + {b^2}}} = {{\left( {3a + b} \right)\left( {9{a^2} – 3ab + {b^2}} \right)} \over {b\left( {3a + b} \right)}} = {{9{a^2} – 3ab + {b^2}} \over b}\).
c) \({{{x^3} – {x^2} – x + 1} \over {{x^4} – 2{x^2} + 1}} = {{{x^2}\left( {x – 1} \right) – \left( {x – 1} \right)} \over {{{\left( {{x^2} – 1} \right)}^2}}} \)
Advertisements (Quảng cáo)
\(= {{\left( {x – 1} \right)\left( {{x^2} – 1} \right)} \over {{{\left( {{x^2} – 1} \right)}^2}}} = {{x – 1} \over {{x^2} – 1}}\)
\( = {{x – 1} \over {\left( {x – 1} \right)\left( {x + 1} \right)}} = {1 \over {x + 1}}.\)
