化简 (4sqrt(x)+1/x)(2-2/(x^{4/3)})

解答

化简

(4 x + \frac{1}{x}) (2 - \frac{2}{x ^{\frac{4}{3}}})

\frac{( 4 x ^{\frac{3}{2}} + 1 ) ( 2 x ^{\frac{4}{3}} - 2 )}{x ^{\frac{7}{3}}}

求解步骤

(4 x + \frac{1}{x}) (2 - \frac{2}{x ^{\frac{4}{3}}})

合并

4 x + \frac{1}{x} : \frac{4 x ^{\frac{3}{2}} + 1}{x}

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

使用分式法则:

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

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

化简

(4 x^{\frac{3}{2}} + 1) (2 - \frac{2}{x ^{\frac{4}{3}}}) : \frac{( 4 x ^{\frac{3}{2}} + 1 ) ( 2 x ^{\frac{4}{3}} - 2 )}{x ^{\frac{4}{3}}}

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

使用分式法则:

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

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

化简

x^{\frac{4}{3}} x : x^{\frac{7}{3}}

= \frac{( 4 x ^{\frac{3}{2}} + 1 ) ( 2 x ^{\frac{4}{3}} - 2 )}{x ^{\frac{7}{3}}}

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s im pl i f y (5 x - 5)^{2}