簡約 1/(\sqrt[4]{x^2-5x)}

解

簡約

\frac{1}{4 x ^{2} - 5 x}

\frac{( x ^{2} - 5 x ) ^{\frac{3}{4}}}{x ^{2} - 5 x}

解答ステップ

\frac{1}{4 x ^{2} - 5 x}

共役で乗じる

\frac{( x ^{2} - 5 x ) ^{\frac{3}{4}}}{( x ^{2} - 5 x ) ^{\frac{3}{4}}}

= \frac{1 \cdot ( x ^{2} - 5 x ) ^{\frac{3}{4}}}{4 x ^{2} - 5 x ( x ^{2} - 5 x ) ^{\frac{3}{4}}}

1 \cdot (x^{2} - 5 x)^{\frac{3}{4}} = (x^{2} - 5 x)^{\frac{3}{4}}

4 x^{2} - 5 x (x^{2} - 5 x)^{\frac{3}{4}} = x^{2} - 5 x

= \frac{( x ^{2} - 5 x ) ^{\frac{3}{4}}}{x ^{2} - 5 x}