erweitern (2-x)^3(1-1/x)^2

Lösung

erweitern

(2 - x)^{3} (1 - \frac{1}{x})^{2}

- x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

Schritte zur Lösung

(2 - x)^{3} (1 - \frac{1}{x})^{2}

Schreibe

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

um:

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

= (2 - x)^{3} \frac{x ^{2} - 2 x + 1}{x ^{2}}

= \frac{x ^{2} - 2 x + 1}{x ^{2}} (2 - x)^{3}

Schreibe

(2 - x)^{3}

um:

8 - 12 x + 6 x^{2} - x^{3}

= \frac{x ^{2} - 2 x + 1}{x ^{2}} (8 - 12 x + 6 x^{2} - x^{3})

Setze Klammern

= \frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 8 + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- 12 x) + \frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 6 x^{2} + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- x^{3})

Vereinfache

\frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 8 + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- 12 x) + \frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 6 x^{2} + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- x^{3}) : - x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

= - x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

e x p an d \frac{6 c ( a - 3 ) ( c + 4 )}{( a - 1 ) ( c + 5 )}

e x p an d x^{\frac{2}{3}} (x - 3)

e x p an d (\frac{d x}{y}) - (2 y - \frac{x}{y ^{2}}) d y

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

e x p an d \frac{x + 3}{2 ( x - 3 )}