展开 (4(x^{0.5}-3)^2)/x

解答

展开

\frac{4 ( x ^{0.5} - 3 ) ^{2}}{x}

4 - \frac{24}{x ^{\frac{1}{2}}} + \frac{36}{x}

求解步骤

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

(x^{\frac{1}{2}} - 3)^{2} = x - 6 x^{\frac{1}{2}} + 9

= \frac{4 ( x - 6 x ^{\frac{1}{2}} + 9 )}{x}

乘开

4 (x - 6 x^{\frac{1}{2}} + 9) : 4 x - 24 x^{\frac{1}{2}} + 36

= \frac{4 x - 24 x ^{\frac{1}{2}} + 36}{x}

使用分式法则:

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

\frac{4 x - 24 x ^{\frac{1}{2}} + 36}{x} = \frac{4 x}{x} - \frac{24 x ^{\frac{1}{2}}}{x} + \frac{36}{x}

= \frac{4 x}{x} - \frac{24 x ^{\frac{1}{2}}}{x} + \frac{36}{x}

消掉

\frac{4 x}{x} : 4

= 4 - \frac{24 x ^{\frac{1}{2}}}{x} + \frac{36}{x}

消掉

\frac{24 x ^{\frac{1}{2}}}{x} : \frac{24}{x ^{\frac{1}{2}}}

= 4 - \frac{24}{x ^{\frac{1}{2}}} + \frac{36}{x}

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