Rút gọn phân thức :
a. \({{{x^4} - {y^4}} \over {{y^3} - {x^3}}}\)
b. \({{\left( {2x - 4} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)\left( {3{x^2} - 27} \right)}}\)
c. \({{2{x^3} + {x^2} - 2x - 1} \over {{x^3} + 2{x^2} - x - 2}}\)
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a. \({{{x^4} - {y^4}} \over {{y^3} - {x^3}}}\) \( = {{\left( {{x^2} + {y^2}} \right)\left( {{x^2} - {y^2}} \right)} \over {\left( {y - x} \right)\left( {{y^2} + xy + {x^2}} \right)}} = {{\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\left( {x - y} \right)} \over {\left( {y - x} \right)\left( {{y^2} + xy + {x^2}} \right)}}\)
\( = - {{\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\left( {x - y} \right)} \over {\left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right)}} = {{\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)} \over {{x^2} + xy + {y^2}}}\)
b. \({{\left( {2x - 4} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)\left( {3{x^2} - 27} \right)}}\) \( = {{2\left( {x - 2} \right)\left( {x + 3} \right)} \over {\left( {x - 2} \right)3\left( {{x^2} - 9} \right)}} = {{2\left( {x + 3} \right)} \over {3\left( {x + 3} \right)\left( {x - 3} \right)}} = {2 \over {3\left( {x - 3} \right)}}\)
c. \({{2{x^3} + {x^2} - 2x - 1} \over {{x^3} + 2{x^2} - x - 2}}\)\( = {{2x\left( {{x^2} - 1} \right) + \left( {{x^2} - 1} \right)} \over {x\left( {{x^2} - 1} \right) + 2\left( {{x^2} - 1} \right)}} = {{\left( {{x^2} - 1} \right)\left( {2x + 1} \right)} \over {\left( {{x^2} - 1} \right)\left( {x + 2} \right)}} = {{2x + 1} \over {x + 2}}\)