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受欢迎的代数 >

化简 (5x^3-x)(1/(x^2)-3)

解答

化简

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

解答

\frac{( 5 x ^{2} - 1 ) ( - 3 x ^{2} + 1 )}{x}

求解步骤

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

合并

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

= (5 x^{3} - x) \frac{- 3 x ^{2} + 1}{x ^{2}}

使用分式法则:

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

= \frac{( 5 x ^{3} - x ) ( - 3 x ^{2} + 1 )}{x ^{2}}

因式分解

5 x^{3} - x : x (5 x^{2} - 1)

= \frac{x ( 5 x ^{2} - 1 ) ( - 3 x ^{2} + 1 )}{x ^{2}}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

x^{2} = xx

= \frac{x ( 5 x ^{2} - 1 ) ( - 3 x ^{2} + 1 )}{xx}

约分:

x

= \frac{( 5 x ^{2} - 1 ) ( - 3 x ^{2} + 1 )}{x}

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