展开-(3(x+3)(x-1))/(x^2)

解答

展开

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

- 3 - \frac{6}{x} + \frac{9}{x ^{2}}

求解步骤

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

乘开

3 (x + 3) (x - 1) : 3 x^{2} + 6 x - 9

= - \frac{3 x ^{2} + 6 x - 9}{x ^{2}}

使用分式法则:

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

\frac{3 x ^{2} + 6 x - 9}{x ^{2}} = - (\frac{3 x ^{2}}{x ^{2}}) - (\frac{6 x}{x ^{2}}) - (- \frac{9}{x ^{2}})

= - (\frac{3 x ^{2}}{x ^{2}}) - (\frac{6 x}{x ^{2}}) - (- \frac{9}{x ^{2}})

去除括号:

(a) = a, - (- a) = a

= - \frac{3 x ^{2}}{x ^{2}} - \frac{6 x}{x ^{2}} + \frac{9}{x ^{2}}

消掉

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

= - 3 - \frac{6 x}{x ^{2}} + \frac{9}{x ^{2}}

消掉

\frac{6 x}{x ^{2}} : \frac{6}{x}

= - 3 - \frac{6}{x} + \frac{9}{x ^{2}}

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

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

e x p an d \frac{100 x ^{3} - 600 x ^{2} + 1200 x - 800}{x}

e x p an d \frac{4 x}{( x - 1 ) ^{2}}

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