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Rút gọn biểu thức :
a. \({{{x^4} – x{y^3}} \over {2xy + {y^2}}}:{{{x^3} + {x^2}y + x{y^2}} \over {2x + y}}\)
b. \({{5{x^2} – 10xy + 5{y^2}} \over {2{x^2} – 2xy + 2{y^2}}}:{{8x – 8y} \over {10{x^3} + 10{y^3}}}\)
a. \({{{x^4} – x{y^3}} \over {2xy + {y^2}}}:{{{x^3} + {x^2}y + x{y^2}} \over {2x + y}}\)\( = {{{x^4} – x{y^3}} \over {2xy + {y^2}}}.{{2x + y} \over {{x^3} + {x^2}y + x{y^2}}} = {{x\left( {{x^3} – {y^3}} \right)\left( {2x + y} \right)} \over {y\left( {2x + y} \right).x\left( {{x^2} + xy + {y^2}} \right)}}\)
\( = {{\left( {x – y} \right)\left( {{x^2} + xy + {y^2}} \right)} \over {y\left( {{x^2} + xy + {y^2}} \right)}} = {{x – y} \over y}\)
b. \({{5{x^2} – 10xy + 5{y^2}} \over {2{x^2} – 2xy + 2{y^2}}}:{{8x – 8y} \over {10{x^3} + 10{y^3}}}\)\( = {{5{x^2} – 10xy + 5{y^2}} \over {2{x^2} – 2xy + 2{y^2}}}.{{10{x^3} + 10{y^3}} \over {8x – 8y}} = {{5\left( {{x^2} – 2xy + {y^2}} \right).10\left( {{x^3} + {y^3}} \right)} \over {2\left( {{x^2} – xy + {y^2}} \right).8\left( {x – y} \right)}}\)
\( = {{25{{\left( {x – y} \right)}^2}\left( {x + y} \right)\left( {{x^2} – xy + {y^2}} \right)} \over {8\left( {{x^2} – xy + {y^2}} \right)\left( {x – y} \right)}} = {{25\left( {x – y} \right)\left( {x + y} \right)} \over 8}\)