vereinfachen (((x^4-1)))/((x-1))

Lösung

vereinfachen

\frac{( ( x ^{4} - 1 ) )}{( x - 1 )}

(x^{2} + 1) (x + 1)

Schritte zur Lösung

\frac{( x ^{4} - 1 )}{x - 1}

Apply rule:

(a) = a

(x^{4} - 1) = x^{4} - 1

= \frac{x ^{4} - 1}{x - 1}

Wende Exponentenregel an

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

Wende Formel zur Differenz von zwei Quadraten an:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2})^{2} - 1^{2} = (x^{2} + 1) (x^{2} - 1)

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

Faktorisiere

x^{2} - 1 : (x + 1) (x - 1)

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

Streiche die gemeinsamen Faktoren:

x - 1

= (x^{2} + 1) (x + 1)

e x p an d (6 x + 4 y)^{3}

f a c t or 3 a^{12} + 1 + 3 a^{6} + a^{18}

e x p an d (6 + x)^{3}

e x p an d (a + b)^{3} + 1

s im pl i f y x (x + y)^{3} - 3 x^{2} y (x + y)