展开 ((x-1)(x^2-4x+5))/x

解答

展开

\frac{( x - 1 ) ( x ^{2} - 4 x + 5 )}{x}

x^{2} - 5 x + 9 - \frac{5}{x}

求解步骤

\frac{( x - 1 ) ( x ^{2} - 4 x + 5 )}{x}

乘开

(x - 1) (x^{2} - 4 x + 5) : x^{3} - 5 x^{2} + 9 x - 5

= \frac{x ^{3} - 5 x ^{2} + 9 x - 5}{x}

使用分式法则:

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

\frac{x ^{3} - 5 x ^{2} + 9 x - 5}{x} = \frac{x ^{3}}{x} - \frac{5 x ^{2}}{x} + \frac{9 x}{x} - \frac{5}{x}

= \frac{x ^{3}}{x} - \frac{5 x ^{2}}{x} + \frac{9 x}{x} - \frac{5}{x}

消掉

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

= x^{2} - \frac{5 x ^{2}}{x} + \frac{9 x}{x} - \frac{5}{x}

消掉

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

= x^{2} - 5 x + \frac{9 x}{x} - \frac{5}{x}

消掉

\frac{9 x}{x} : 9

= x^{2} - 5 x + 9 - \frac{5}{x}

e x p an d \frac{1}{x \cdot ( x - 118 )}

e x p an d A (6, - 3) B (- 8, - 5)

e x p an d r x (r x - 1) k e^{r x - 2}

e x p an d (x^{3} + 7) e^{2}

e x p an d 3 - x - \frac{( 3 - x ) ^{3}}{3}