展开 (((z-1)*(z-0.586)))/(z^2)

解答

展开

\frac{( ( z - 1 ) \cdot ( z - 0.586 ) )}{z ^{2}}

1 - \frac{1.586}{z} + \frac{0.586}{z ^{2}}

求解步骤

\frac{( z - 1 ) ( z - 0.586 )}{z ^{2}}

乘开

(z - 1) (z - 0.586) : z^{2} - 1.586 z + 0.586

= \frac{z ^{2} - 1.586 z + 0.586}{z ^{2}}

使用分式法则:

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

\frac{z ^{2} - 1.586 z + 0.586}{z ^{2}} = \frac{z ^{2}}{z ^{2}} - \frac{1.586 z}{z ^{2}} + \frac{0.586}{z ^{2}}

= \frac{z ^{2}}{z ^{2}} - \frac{1.586 z}{z ^{2}} + \frac{0.586}{z ^{2}}

使用法则

\frac{a}{a} = 1

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

= 1 - \frac{1.586 z}{z ^{2}} + \frac{0.586}{z ^{2}}

消掉

\frac{1.586 z}{z ^{2}} : \frac{1.586}{z}

= 1 - \frac{1.586}{z} + \frac{0.586}{z ^{2}}

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