Để có các phân thức có cùng mẫu, ta cần điền vào chỗ trống \(\frac{{x - 1}}{{{x^2}\left( {x + 1} \right)}} = \frac{{x - 1}}{{...}}\); \(\frac{{3x}}{{x + 1}} = \frac{{...}}{{{x^2}\left( {x + 1} \right)}}\) ra sao?

A. x²(x – y);

A. \(\frac{{x\left( {x + 3} \right)}}{{2\left( {{x^2} - 9} \right)}}\) và \(\frac{8}{{\left( {{x^2} - 9} \right).2}}\);

B. \(\frac{x}{{2\left( {{x^2} - 9} \right)}}\) và \[\frac{4}{{\left( {{x^2} - 9} \right)\,.\,2}}\];

C. \(\frac{{x\left( {x + 3} \right)}}{{2x - 6}}\) và \(\frac{8}{{{x^2} - 9}}\);

D. \(\frac{{2x}}{{2\left( {{x^2} - 9} \right)}}\) và \(\frac{{4\left( {x - 3} \right)}}{{\left( {{x^2} - 9} \right)}}\).

A. (x – y)² ;

A. \(\frac{{{x^2} - {y^2}}}{{{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{{x^2} - 2xy + {y^2}}}{{{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{ - 1}}{{{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\);

B. \(\frac{{{x^2} - {y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{{x^2} - 2xy + {y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{ - 1}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\);

C. \(\frac{{2{x^2} - 2{y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{{x^2} - 2xy + {y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{2}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\);

D. \[\frac{{{x^2} - {y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\]; \(\frac{{{x^2} - 2xy + {y^2}}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\); \(\frac{{ - 2}}{{2{{\left( {x - y} \right)}^2}\left( {x + y} \right)}}\).

B.\(\frac{4}{{2\left( {x - 3} \right)\left( {x + 3} \right)}}\);

A. (x + 3)³ ;

A. \(\frac{3}{{5{x^2}yz}} = \frac{{12yz}}{{20{x^2}{y^2}{z^2}}}\) ; \(\frac{5}{{4{y^2}z}}\)= \(\frac{{25{x^2}z}}{{20{x^2}{y^2}{z^2}}}\); \(\frac{6}{{x{z^2}}}\) = \(\frac{{120x{y^2}}}{{20{x^2}{y^2}{z^2}}}\);

B. \(\frac{3}{{5{x^2}yz}}\) = \(\frac{{12yz}}{{20{x^2}{y^2}{z^2}}}\); \(\frac{5}{{4{y^2}z}}\)= \(\frac{{25{x^2}z}}{{20{x^2}{y^2}{z^2}}}\); \(\frac{6}{{x{z^2}}}\) = \(\frac{{x{y^2}}}{{20{x^2}{y^2}{z^2}}}\);

C. \(\frac{3}{{5{x^2}yz}}\) = \(\frac{{3yz}}{{{x^2}{y^2}{z^2}}}\); \(\frac{5}{{4{y^2}z}}\)= \(\frac{{5{x^2}z}}{{{x^2}{y^2}{z^2}}}\); \(\frac{6}{{x{z^2}}}\) = \(\frac{{x{y^2}}}{{{x^2}{y^2}{z^2}}}\);

D. \(\frac{3}{{5{x^2}yz}}\) = \(\frac{{3yz}}{{20{x^2}{y^2}{z^2}}}\); \(\frac{5}{{4{y^2}z}}\)= \(\frac{{20{x^2}z}}{{20{x^2}{y^2}{z^2}}}\); \(\frac{6}{{x{z^2}}}\) = \(\frac{{120x{y^2}}}{{20{x^2}{y^2}{z^2}}}\).