erweitern ((z-1)/(zT))^2

Lösung

erweitern

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

\frac{1}{T ^{2}} - \frac{2}{z T ^{2}} + \frac{1}{z ^{2} T ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

= \frac{( z - 1 ) ^{2}}{( z T ) ^{2}}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

(z T)^{2} = z^{2} T^{2}

= \frac{( z - 1 ) ^{2}}{z ^{2} T ^{2}}

(z - 1)^{2} = z^{2} - 2 z + 1

= \frac{z ^{2} - 2 z + 1}{z ^{2} T ^{2}}

Wende Bruchregel an:

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

\frac{z ^{2} - 2 z + 1}{z ^{2} T ^{2}} = \frac{z ^{2}}{z ^{2} T ^{2}} - \frac{2 z}{z ^{2} T ^{2}} + \frac{1}{z ^{2} T ^{2}}

= \frac{z ^{2}}{z ^{2} T ^{2}} - \frac{2 z}{z ^{2} T ^{2}} + \frac{1}{z ^{2} T ^{2}}

Streiche

\frac{z ^{2}}{z ^{2} T ^{2}} : \frac{1}{T ^{2}}

= \frac{1}{T ^{2}} - \frac{2 z}{z ^{2} T ^{2}} + \frac{1}{z ^{2} T ^{2}}

Streiche

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

= \frac{1}{T ^{2}} - \frac{2}{z T ^{2}} + \frac{1}{z ^{2} T ^{2}}

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