vereinfachen (x-1/a)(x-1/b)(x-1/c)

Lösung

vereinfachen

(x - \frac{1}{a}) (x - \frac{1}{b}) (x - \frac{1}{c})

\frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c a}

Schritte zur Lösung

(x - \frac{1}{a}) (x - \frac{1}{b}) (x - \frac{1}{c})

Füge zusammen:

x - \frac{1}{a} : \frac{x a - 1}{a}

= \frac{x a - 1}{a} (x - \frac{1}{b}) (x - \frac{1}{c})

Wende Bruchregel an:

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

= \frac{( x a - 1 ) ( x - \frac{1}{b} ) ( x - \frac{1}{c} )}{a}

Vereinfache

(x a - 1) (x - \frac{1}{b}) (x - \frac{1}{c}) : \frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c}

= \frac{\frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c}}{a}

Wende Bruchregel an:

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

= \frac{( x a - 1 ) ( x b - 1 ) ( x c - 1 )}{b c a}

e x p an d \frac{( x ^{2} - 2 x + 3 ) ( 2 x + 3 )}{( x - 2 ) ( x + 5 )}

e x p an d so l v e (30 - 2 h) (30 - h) (h)

e x p an d (3 x) l e f t (- 118.33 x - 10 x^{2})

e x p an d \frac{x ^{2} + 4}{( x ^{2} - 4 ) ^{2}}

e x p an d (1 + \frac{1}{2} x)^{4}