展开 (x(x+1)+1)/x

解答

展开

\frac{x ( x + 1 ) + 1}{x}

x + 1 + \frac{1}{x}

求解步骤

\frac{x ( x + 1 ) + 1}{x}

乘开

x (x + 1) + 1 : x^{2} + x + 1

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

使用分式法则:

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

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

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

使用法则

\frac{a}{a} = 1

\frac{x}{x} = 1

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

消掉

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

= x + 1 + \frac{1}{x}

e x p an d \frac{8 s ^{2} - 1920}{( s ^{2} + 400 ) ( s ^{2} + 144 )}

e x p an d \frac{x ^{3}}{9 ( x - 8 ) ^{3}}

\frac{\partial}{\partial u} ((g (u, v, w)) (uv + w^{2}))

e x p an d C (- 3, - 4) P (7, - 1)

e x p an d (2 e^{3 x} + 6 e^{3 x} x + e^{x} + e^{x} x)^{2}