Thực hiện các phép chia phân thức sau:
a) \(\frac{{5x}}{{6y}}:\frac{{10{x^2}}}{9}\);
b) \(\frac{{ - xy}}{8}:\frac{{{x^2}}}{{4y}}\);
c) \(\frac{7}{{9{x^2}}}:\frac{{ - 14y}}{{3{x^3}}}\);
d) \(\frac{{3x}}{{2y}}:\left( {6{x^2}{y^2}} \right)\).
Thực hiện các phép chia phân thức sau:
a) \(\frac{{5x}}{{6y}}:\frac{{10{x^2}}}{9}\);
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b) \(\frac{{ - xy}}{8}:\frac{{{x^2}}}{{4y}}\);
c) \(\frac{7}{{9{x^2}}}:\frac{{ - 14y}}{{3{x^3}}}\);
d) \(\frac{{3x}}{{2y}}:\left( {6{x^2}{y^2}} \right)\).
a) \(\frac{{5x}}{{6y}}:\frac{{10{x^2}}}{9} = \frac{{5x}}{{6y}}.\frac{9}{{10{x^2}}} = \frac{{5x.3.3}}{{3.2y.5.2x.x}} = \frac{3}{{4xy}}\);
b) \(\frac{{ - xy}}{8}:\frac{{{x^2}}}{{4y}} = \frac{{ - xy}}{{4.2}}.\frac{{4y}}{{x.x}} = \frac{{ - xy.4y}}{{4.2.x.x}} = \frac{{ - {y^2}}}{{2x}}\);
c) \(\frac{7}{{9{x^2}}}:\frac{{ - 14y}}{{3{x^3}}} = \frac{7}{{3.3{x^2}}}.\frac{{3{x^2}.x}}{{ - 2.7y}} = \frac{{7.3{x^2}.x}}{{3.3{x^2}.\left( { - 2} \right).7y}} = \frac{{ - x}}{{6y}}\);
d) \(\frac{{3x}}{{2y}}:\left( {6{x^2}{y^2}} \right) = \frac{{3x}}{{2y}}.\frac{1}{{6{x^2}{y^2}}} = \frac{{3x}}{{2y.2.3x.x.{y^2}}} = \frac{1}{{4x{y^3}}}\).