化简 (4sqrt(x)+1/x)(2x-6/(\sqrt[3]{x)})

解答

化简

(4 x + \frac{1}{x}) (2 x - \frac{6}{3 x})

\frac{8 6 x ^{17} - 24 x ^{3} + 2 3 x ^{4} - 6}{3 x ^{4}}

求解步骤

(4 x + \frac{1}{x}) (2 x - \frac{6}{3 x})

合并

4 x + \frac{1}{x} : \frac{4 x x + 1}{x}

= \frac{4 x x + 1}{x} (2 x - \frac{6}{3 x})

使用分式法则:

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

= \frac{( 4 x x + 1 ) ( 2 x - \frac{6}{3 x} )}{x}

化简

(4 x x + 1) (2 x - \frac{6}{3 x}) : \frac{8 x ^{\frac{17}{6}} - 24 x ^{\frac{3}{2}} + 2 x ^{\frac{4}{3}} - 6}{3 x}

= \frac{\frac{8 x ^{\frac{17}{6}} - 24 x ^{\frac{3}{2}} + 2 x ^{\frac{4}{3}} - 6}{3 x}}{x}

使用分式法则:

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

= \frac{8 x ^{\frac{17}{6}} - 24 x ^{\frac{3}{2}} + 2 x ^{\frac{4}{3}} - 6}{3 x x}

化简

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

= \frac{8 x ^{\frac{17}{6}} - 24 x ^{\frac{3}{2}} + 2 x ^{\frac{4}{3}} - 6}{x ^{\frac{4}{3}}}

x^{\frac{17}{6}} = 6 x^{17}

= \frac{8 6 x ^{17} - 24 x ^{3} + 2 3 x ^{4} - 6}{3 x ^{4}}

x^{\frac{3}{2}} = x^{3}

= \frac{8 6 x ^{17} - 24 x ^{3} + 2 3 x ^{4} - 6}{3 x ^{4}}

x^{\frac{4}{3}} = 3 x^{4}

= \frac{8 6 x ^{17} - 24 x ^{3} + 2 3 x ^{4} - 6}{3 x ^{4}}

x^{\frac{4}{3}} = 3 x^{4}

= \frac{8 6 x ^{17} - 24 x ^{3} + 2 3 x ^{4} - 6}{3 x ^{4}}

\int (8 x - 3) \cdot ln (x) d x

s l o p e (7.7) (2.1)

l a pl a ce t r an s f or m \frac{t ^{2} e ^{- 2 t}}{2}

\int \frac{1}{u ^{2} - 3} d u

\frac{d}{d x} (\frac{x + 8}{3})