展开 ((1-x)^3)/(x^2)

解答

展开

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

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

求解步骤

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

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

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

使用分式法则:

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

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

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

消掉

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

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

消掉

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

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

消掉

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

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

e x p an d (- e^{- x} sin (x) + e^{- x} cos (x))^{2}

e x p an d \frac{12}{x ( x - 4 )}

e x p an d (2, - 3) y (4, 2)

e x p an d (2 x^{3} - x y^{2} - 2 y + 3) d x + (x^{2} y + 2 x)

s im pl i f y (a + \frac{1}{4}) (a - \frac{1}{4})