Đề bài

Rút gọn các phân thức sau: a) \(\dfrac{{3{x^2}y}}{{2x{y^5}}}\) b) \(\dfrac{{3{x^2} - 3x}}{{x - 1}}\)  c) \(\dfrac{{a{b^2} - {a^2}b}}{{2{a^2} + a}}\) d) \(\dfrac{{12\left( {{x^4} - 1} \right)}}{{18\left( {{x^2} - 1} \right)}}\)

Lời giải chi tiết

a) \(\dfrac{{3{x^2}y}}{{2x{y^5}}}\)\( = \dfrac{{xy.3x}}{{xy.2{y^4}}} = \dfrac{{3x}}{{2{y^4}}}\)b) \(\dfrac{{3{x^2} - 3x}}{{x - 1}}\) \( = \dfrac{{3x\left( {x - 1} \right)}}{{x - 1}} = 3x\)c) \(\dfrac{{a{b^2} - {a^2}b}}{{2{a^2} + a}}\) \( = \dfrac{{a\left( {{b^2} - ab} \right)}}{{a\left( {2a + 1} \right)}} = \dfrac{{{b^2} - ab}}{{2a + 1}}\)d) \(\dfrac{{12\left( {{x^4} - 1} \right)}}{{18\left( {{x^2} - 1} \right)}}\) \( = \dfrac{{6.2.\left( {{x^2} - 1} \right)\left( {{x^2} + 1} \right)}}{{6.3.\left( {{x^2} - 1} \right)}} = \dfrac{{2\left( {{x^2} + 1} \right)}}{3}\)