erweitern ((x^2-x+2)^2)/x

Lösung

erweitern

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

x^{3} - 2 x^{2} + 5 x - 4 + \frac{4}{x}

Schritte zur Lösung

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

(x^{2} - x + 2)^{2} = x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 4

= \frac{x ^{4} - 2 x ^{3} + 5 x ^{2} - 4 x + 4}{x}

Wende Bruchregel an:

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

\frac{x ^{4} - 2 x ^{3} + 5 x ^{2} - 4 x + 4}{x} = \frac{x ^{4}}{x} - \frac{2 x ^{3}}{x} + \frac{5 x ^{2}}{x} - \frac{4 x}{x} + \frac{4}{x}

= \frac{x ^{4}}{x} - \frac{2 x ^{3}}{x} + \frac{5 x ^{2}}{x} - \frac{4 x}{x} + \frac{4}{x}

\frac{x ^{4}}{x} = x^{3}

\frac{2 x ^{3}}{x} = 2 x^{2}

\frac{5 x ^{2}}{x} = 5 x

\frac{4 x}{x} = 4

= x^{3} - 2 x^{2} + 5 x - 4 + \frac{4}{x}

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