展开 (((x+1))/x)^2

解答

展开

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

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

求解步骤

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

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

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

使用分式法则:

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

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

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

使用法则

\frac{a}{a} = 1

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

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

消掉

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

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

e x p an d (x z^{^{'}} + z) (2 z + 1)

e x p an d P (1, - 3, 2) Q (2, 1, - 1)

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

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

e x p an d \frac{( x + 6 ) ^{2}}{4}