展开 ((x^3+1)(x-2))/(x^2)

解答

展开

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

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

求解步骤

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

乘开

(x^{3} + 1) (x - 2) : x^{4} - 2 x^{3} + x - 2

= \frac{x ^{4} - 2 x ^{3} + x - 2}{x ^{2}}

使用分式法则:

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

\frac{x ^{4} - 2 x ^{3} + x - 2}{x ^{2}} = \frac{x ^{4}}{x ^{2}} - \frac{2 x ^{3}}{x ^{2}} + \frac{x}{x ^{2}} - \frac{2}{x ^{2}}

= \frac{x ^{4}}{x ^{2}} - \frac{2 x ^{3}}{x ^{2}} + \frac{x}{x ^{2}} - \frac{2}{x ^{2}}

消掉

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

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

消掉

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

= x^{2} - 2 x + \frac{x}{x ^{2}} - \frac{2}{x ^{2}}

消掉

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

= x^{2} - 2 x + \frac{1}{x} - \frac{2}{x ^{2}}

e x p an d \frac{λ ( λ - 1 ) ( λ - 2 ) ( λ - 3 )}{24}

e x p an d (- 8, - 1) y (- 6, 5) (- 6, 5)

e x p an d \frac{( 34 x - 442 ) ^{2}}{28561}

e x p an d \frac{x ^{2} + 2 x - 2}{( x + 1 ) ^{2}}

e x p an d - \frac{5}{2 ( 2 - 5 x )}