展开 1/(\sqrt[5]{1+x)}

解答

展开

\frac{1}{5 1 + x}

\frac{( 1 + x ) ^{\frac{4}{5}}}{1 + x}

求解步骤

\frac{1}{5 1 + x}

乘以共轭根式

\frac{( 1 + x ) ^{\frac{4}{5}}}{( 1 + x ) ^{\frac{4}{5}}}

= \frac{1 \cdot ( 1 + x ) ^{\frac{4}{5}}}{5 1 + x ( 1 + x ) ^{\frac{4}{5}}}

1 \cdot (1 + x)^{\frac{4}{5}} = (1 + x)^{\frac{4}{5}}

5 1 + x (1 + x)^{\frac{4}{5}} = 1 + x

= \frac{( 1 + x ) ^{\frac{4}{5}}}{1 + x}

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