vereinfachen (a-1/a)(a+1/a)

Lösung

vereinfachen

(a - \frac{1}{a}) (a + \frac{1}{a})

\frac{( a ^{2} - 1 ) ( a ^{2} + 1 )}{a ^{2}}

Schritte zur Lösung

(a - \frac{1}{a}) (a + \frac{1}{a})

Füge zusammen:

a - \frac{1}{a} : \frac{a ^{2} - 1}{a}

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

Wende Bruchregel an:

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

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

Vereinfache

(a^{2} - 1) (a + \frac{1}{a}) : \frac{( a ^{2} - 1 ) ( a ^{2} + 1 )}{a}

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

Wende Bruchregel an:

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

= \frac{( a ^{2} - 1 ) ( a ^{2} + 1 )}{aa}

Wende Exponentenregel an:

aa = a^{2}

aa = a^{2}

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

e x p an d - 2 (3 - 5)

e x p an d 3 (10 - 5)

e x p an d \frac{11 x - 8}{x ( x - 4 )}

s im pl i f y (2 + 2 a) \cdot (2 - 2 a)

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