化简 (x-1/a)(x-1/b)(x-1/c)

解答

化简

(x - \frac{1}{a}) (x - \frac{1}{b}) (x - \frac{1}{c})

\frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c a}

求解步骤

(x - \frac{1}{a}) (x - \frac{1}{b}) (x - \frac{1}{c})

合并

x - \frac{1}{a} : \frac{x a - 1}{a}

= \frac{x a - 1}{a} (x - \frac{1}{b}) (x - \frac{1}{c})

使用分式法则:

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

= \frac{( x a - 1 ) ( x - \frac{1}{b} ) ( x - \frac{1}{c} )}{a}

化简

(x a - 1) (x - \frac{1}{b}) (x - \frac{1}{c}) : \frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c}

= \frac{\frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c}}{a}

使用分式法则:

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

= \frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c a}

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