展开 ((x^2+3x-28)(x-4))/(2x^3)

解答

展开

\frac{( x ^{2} + 3 x - 28 ) ( x - 4 )}{2 x ^{3}}

\frac{1}{2} - \frac{1}{2 x} - \frac{20}{x ^{2}} + \frac{56}{x ^{3}}

求解步骤

\frac{( x ^{2} + 3 x - 28 ) ( x - 4 )}{2 x ^{3}}

乘开

(x^{2} + 3 x - 28) (x - 4) : x^{3} - x^{2} - 40 x + 112

= \frac{x ^{3} - x ^{2} - 40 x + 112}{2 x ^{3}}

使用分式法则:

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

\frac{x ^{3} - x ^{2} - 40 x + 112}{2 x ^{3}} = \frac{x ^{3}}{2 x ^{3}} - \frac{x ^{2}}{2 x ^{3}} - \frac{40 x}{2 x ^{3}} + \frac{112}{2 x ^{3}}

= \frac{x ^{3}}{2 x ^{3}} - \frac{x ^{2}}{2 x ^{3}} - \frac{40 x}{2 x ^{3}} + \frac{112}{2 x ^{3}}

\frac{x ^{3}}{2 x ^{3}} = \frac{1}{2}

\frac{x ^{2}}{2 x ^{3}} = \frac{1}{2 x}

\frac{40 x}{2 x ^{3}} = \frac{20}{x ^{2}}

\frac{112}{2 x ^{3}} = \frac{56}{x ^{3}}

= \frac{1}{2} - \frac{1}{2 x} - \frac{20}{x ^{2}} + \frac{56}{x ^{3}}

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