erweitern ((x-1)^2+2(x-1)x^{1/13})/(13x^{12/13)}

Lösung

erweitern

\frac{( x - 1 ) ^{2} + 2 ( x - 1 ) x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}}

\frac{x ^{\frac{14}{13}}}{13} - \frac{2 x ^{\frac{1}{13}}}{13} + \frac{1}{13 x ^{\frac{12}{13}}} + \frac{2 x ^{\frac{2}{13}}}{13} - \frac{2}{13 x ^{\frac{11}{13}}}

Schritte zur Lösung

\frac{( x - 1 ) ^{2} + 2 ( x - 1 ) x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}}

Multipliziere aus

(x - 1)^{2} + 2 (x - 1) x^{\frac{1}{13}} : x^{2} - 2 x + 1 + 2 x^{\frac{14}{13}} - 2 x^{\frac{1}{13}}

= \frac{x ^{2} - 2 x + 1 + 2 x ^{\frac{14}{13}} - 2 x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}}

Wende Bruchregel an:

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

\frac{x ^{2} - 2 x + 1 + 2 x ^{\frac{14}{13}} - 2 x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}} = \frac{x ^{2}}{13 x ^{\frac{12}{13}}} - \frac{2 x}{13 x ^{\frac{12}{13}}} + \frac{1}{13 x ^{\frac{12}{13}}} + \frac{2 x ^{\frac{14}{13}}}{13 x ^{\frac{12}{13}}} - \frac{2 x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}}

= \frac{x ^{2}}{13 x ^{\frac{12}{13}}} - \frac{2 x}{13 x ^{\frac{12}{13}}} + \frac{1}{13 x ^{\frac{12}{13}}} + \frac{2 x ^{\frac{14}{13}}}{13 x ^{\frac{12}{13}}} - \frac{2 x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}}

\frac{x ^{2}}{13 x ^{\frac{12}{13}}} = \frac{x ^{\frac{14}{13}}}{13}

\frac{2 x}{13 x ^{\frac{12}{13}}} = \frac{2 x ^{\frac{1}{13}}}{13}

\frac{2 x ^{\frac{14}{13}}}{13 x ^{\frac{12}{13}}} = \frac{2 x ^{\frac{2}{13}}}{13}

\frac{2 x ^{\frac{1}{13}}}{13 x ^{\frac{12}{13}}} = \frac{2}{13 x ^{\frac{11}{13}}}

= \frac{x ^{\frac{14}{13}}}{13} - \frac{2 x ^{\frac{1}{13}}}{13} + \frac{1}{13 x ^{\frac{12}{13}}} + \frac{2 x ^{\frac{2}{13}}}{13} - \frac{2}{13 x ^{\frac{11}{13}}}

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