a) \(\displaystyle{{{x^4} - x{y^3}} \over {2xy + {y^2}}}:{{{x^3} + {x^2}y + x{y^2}} \over {2x + y}}\)
\(\displaystyle = {{{x^4} - x{y^3}} \over {2xy + {y^2}}}.{{2x + y} \over {{x^3} + {x^2}y + x{y^2}}} \)
\(\displaystyle= {{x\left( {{x^3} - {y^3}} \right)\left( {2x + y} \right)} \over {y\left( {2x + y} \right).x\left( {{x^2} + xy + {y^2}} \right)}}\)
\(\displaystyle = {{\left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right)} \over {y\left( {{x^2} + xy + {y^2}} \right)}} = {{x - y} \over y}\)
b) \(\displaystyle{{5{x^2} - 10xy + 5{y^2}} \over {2{x^2} - 2xy + 2{y^2}}}:{{8x - 8y} \over {10{x^3} + 10{y^3}}}\)
\(\displaystyle = {{5{x^2} - 10xy + 5{y^2}} \over {2{x^2} - 2xy + 2{y^2}}}.{{10{x^3} + 10{y^3}} \over {8x - 8y}} \)
\(\displaystyle= {{5\left( {{x^2} - 2xy + {y^2}} \right).10\left( {{x^3} + {y^3}} \right)} \over {2\left( {{x^2} - xy + {y^2}} \right).8\left( {x - y} \right)}}\)
\(\displaystyle = {{25{{\left( {x - y} \right)}^2}\left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right)} \over {8\left( {{x^2} - xy + {y^2}} \right)\left( {x - y} \right)}} \)
\(\displaystyle= {{25\left( {x - y} \right)\left( {x + y} \right)} \over 8}\)
