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受欢迎的代数 >

展开 ((10x^2-x+3)(x-5))/(2x^2)

解答

展开

\frac{( 10 x ^{2} - x + 3 ) ( x - 5 )}{2 x ^{2}}

解答

5 x - \frac{51}{2} + \frac{4}{x} - \frac{15}{2 x ^{2}}

求解步骤

\frac{( 10 x ^{2} - x + 3 ) ( x - 5 )}{2 x ^{2}}

乘开

(10 x^{2} - x + 3) (x - 5) : 10 x^{3} - 51 x^{2} + 8 x - 15

= \frac{10 x ^{3} - 51 x ^{2} + 8 x - 15}{2 x ^{2}}

使用分式法则:

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

\frac{10 x ^{3} - 51 x ^{2} + 8 x - 15}{2 x ^{2}} = \frac{10 x ^{3}}{2 x ^{2}} - \frac{51 x ^{2}}{2 x ^{2}} + \frac{8 x}{2 x ^{2}} - \frac{15}{2 x ^{2}}

= \frac{10 x ^{3}}{2 x ^{2}} - \frac{51 x ^{2}}{2 x ^{2}} + \frac{8 x}{2 x ^{2}} - \frac{15}{2 x ^{2}}

消掉

\frac{10 x ^{3}}{2 x ^{2}} : 5 x

= 5 x - \frac{51 x ^{2}}{2 x ^{2}} + \frac{8 x}{2 x ^{2}} - \frac{15}{2 x ^{2}}

消掉

\frac{51 x ^{2}}{2 x ^{2}} : \frac{51}{2}

= 5 x - \frac{51}{2} + \frac{8 x}{2 x ^{2}} - \frac{15}{2 x ^{2}}

消掉

\frac{8 x}{2 x ^{2}} : \frac{4}{x}

= 5 x - \frac{51}{2} + \frac{4}{x} - \frac{15}{2 x ^{2}}

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