展開する (6x-5)/(3(x-1)^{2/3)(2x-1)^{1/3}}

解

展開する

\frac{6 x - 5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}

\frac{2 x}{( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}} - \frac{5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}

解答ステップ

\frac{6 x - 5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{6 x - 5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}} = \frac{6 x}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}} - \frac{5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}

= \frac{6 x}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}} - \frac{5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}

数を割る:

\frac{6}{3} = 2

= \frac{2 x}{( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}} - \frac{5}{3 ( x - 1 ) ^{\frac{2}{3}} ( 2 x - 1 ) ^{\frac{1}{3}}}