化简 (1+s/(10))(1+s/(100))(1+s/(1000))

解答

化简

(1 + \frac{s}{10}) (1 + \frac{s}{100}) (1 + \frac{s}{1000})

\frac{( 10 + s ) ( 100 + s ) ( 1000 + s )}{1000000}

求解步骤

(1 + \frac{s}{10}) (1 + \frac{s}{100}) (1 + \frac{s}{1000})

合并

1 + \frac{s}{10} : \frac{10 + s}{10}

= \frac{10 + s}{10} (1 + \frac{s}{100}) (1 + \frac{s}{1000})

使用分式法则:

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

= \frac{( 10 + s ) ( 1 + \frac{s}{100} ) ( 1 + \frac{s}{1000} )}{10}

化简

(10 + s) (1 + \frac{s}{100}) (1 + \frac{s}{1000}) : \frac{( 10 + s ) ( 100 + s ) ( 1000 + s )}{100000}

= \frac{\frac{( 10 + s ) ( 100 + s ) ( 1000 + s )}{100000}}{10}

使用分式法则:

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

= \frac{( 10 + s ) ( 100 + s ) ( 1000 + s )}{100000 \cdot 10}

数字相乘:

100000 \cdot 10 = 1000000

= \frac{( 10 + s ) ( 100 + s ) ( 1000 + s )}{1000000}

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