展开 1+3/(2+\frac{4){1-1/4}}

解答

展开

1 + \frac{3}{2 + \frac{4}{1 - \frac{1}{4}}}

\frac{31}{22}

十进制

1.40909 \dots

求解步骤

1 + \frac{3}{2 + \frac{4}{1 - \frac{1}{4}}}

\frac{3}{2 + \frac{4}{1 - \frac{1}{4}}} = \frac{9}{22}

= 1 + \frac{9}{22}

将项转换为分式:

1 = \frac{1 \cdot 22}{22}

= \frac{1 \cdot 22}{22} + \frac{9}{22}

因为分母相等，所以合并分式:

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

= \frac{1 \cdot 22 + 9}{22}

1 \cdot 22 + 9 = 31

= \frac{31}{22}

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