Đề bài

Rút gọn các phân thức sau: a) \(\frac{{6ab}}{{ - 4ac}}\); b) \(\frac{{ - {a^4}b}}{{ - 2{a^2}{b^3}}}\); c) \(\frac{{5a\left( {a - b} \right)}}{{10b\left( {b - a} \right)}}\); d) \(\frac{{3a\left( {1 - a} \right)}}{{9{{\left( {a - 1} \right)}^2}}}\).

Lời giải chi tiết

a) \(\frac{{6ab}}{{ - 4ac}} = \frac{{3.2a.b}}{{ - 2.2a.c}} = \frac{{ - 3b}}{{2c}}\); b) \(\frac{{ - {a^4}b}}{{ - 2{a^2}{b^3}}} = \frac{{ - {a^2}.{a^2}b}}{{ - 2.{a^2}.b.{b^2}}} = \frac{{{a^2}}}{{2{b^2}}}\); c) \(\frac{{5a\left( {a - b} \right)}}{{10b\left( {b - a} \right)}} = \frac{{5a\left( {a - b} \right)}}{{ - 5.2b\left( {a - b} \right)}} = \frac{{ - a}}{{2b}}\);

d) \(\frac{{3a\left( {1 - a} \right)}}{{9{{\left( {a - 1} \right)}^2}}} = \frac{{3a\left( {1 - a} \right)}}{{9{{\left( {1 - a} \right)}^2}}}  = \frac{{3a\left( {1 - a} \right)}}{{{3^2}\left( {1 - a} \right)\left( {1 - a} \right)}} = \frac{a}{{3\left( {1 - a} \right)}}\).