Đề bài

Thực hiện các phép chia phân thức sau: a) \(\dfrac{{5x}}{{4{y^3}}}:\left( { - \dfrac{{{x^4}}}{{20y}}} \right)\)                  b) \(\dfrac{{{x^2} - 16}}{{x + 4}} :\dfrac{{2x - 8}}{x}\)                      c) \(\dfrac{{2x + 6}}{{{x^3} - 8}}:\dfrac{{{{\left( {x + 3} \right)}^3}}}{{2x - 4}}\)  

Lời giải chi tiết

a) \(\dfrac{{5x}}{{4{y^3}}}:\left( { - \dfrac{{{x^4}}}{{20y}}} \right)\) \( = \dfrac{{5x}}{{4{y^3}}} \cdot \dfrac{{ - 20y}}{{{x^4}}} \\= \dfrac{{ - 100xy}}{{4{x^4}{y^3}}} \\= \dfrac{{ - 25}}{{{x^3}{y^2}}}\) b) \(\dfrac{{{x^2} - 16}}{{x + 4}} :\dfrac{{2x - 8}}{x}\) \( = \dfrac{{\left( {x - 4} \right)\left( {x + 4} \right)}}{{x + 4}} \cdot \dfrac{x}{{2x - 8}} \\= \dfrac{{\left( {x - 4} \right)\left( {x + 4} \right)}}{{x + 4}} \cdot \dfrac{x}{{2\left( {x - 4} \right)}} \\= \dfrac{x}{2}\) c) \(\dfrac{{2x + 6}}{{{x^3} - 8}}:\dfrac{{{{\left( {x + 3} \right)}^3}}}{{2x - 4}}\) \( = \dfrac{{2\left( {x + 3} \right)}}{{\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)}} \cdot \dfrac{{2\left( {x - 2} \right)}}{{{{\left( {x + 3} \right)}^3}}} \\= \dfrac{4}{{{{\left( {x + 3} \right)}^2}\left( {{x^2} + 2x + 4} \right)}}\)