(dfrac{{2{x^2} + 2x}}{{3{x^3} - 9{x^2}y + 9x{y^2} - 3{y^3}}};,)(dfrac{2}{{{y^2} - xy}})
Giải chi tiết:
(dfrac{{2{x^2} + 2x}}{{3{x^3} - 9{x^2}y + 9x{y^2} - 3{y^3}}};,,dfrac{2}{{{y^2} - xy}})
Ta có:
(begin{array}{l},,,,,3{x^3} - 9{x^2}y + 9x{y^2} - 3{y^3}\ = 3left( {{x^3} - 3{x^2}y + 3x{y^2} - {y^3}} right) = 3{left( {x - y} right)^3}\{y^2} - xy = yleft( {y - x} right) = - yleft( {x - y} right)end{array})
( Rightarrow ) MTC: (3y{left( {x - y} right)^3})
NTP1: (y)
NTP2: ( - 3{left( {x - y} right)^2})
(begin{array}{l} Rightarrow dfrac{{2{x^2} + 2x}}{{3{x^3} - 9{x^2}y + 9x{y^2} - 3{y^3}}} = dfrac{{2xleft( {x + 1} right)}}{{3{{left( {x - y} right)}^3}}} = dfrac{{2xyleft( {x + 1} right)}}{{3y{{left( {x - y} right)}^3}}}\,dfrac{2}{{{y^2} - xy}} = dfrac{{2.left[ { - 3{{left( {x - y} right)}^2}} right]}}{{yleft( {y - x} right).left[ { - 3{{left( {x - y} right)}^2}} right]}} = dfrac{{ - 6{{left( {x - y} right)}^2}}}{{3y{{left( {x - y} right)}^3}}}end{array})
Chọn A.