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Beliebt Algebra >

faktorisieren (x-3)^{7/2}-9(x-3)^{3/2}

Lösung

faktorisieren

(x - 3)^{\frac{7}{2}} - 9 (x - 3)^{\frac{3}{2}}

Lösung

x (x - 6) (x - 3)^{\frac{3}{2}}

Schritte zur Lösung

(x - 3)^{\frac{7}{2}} - 9 (x - 3)^{\frac{3}{2}}

Schreibe

(x - 3)^{\frac{7}{2}}

um:

(x - 3)^{7}

= (x - 3)^{7} - 9 (x - 3)^{\frac{3}{2}}

Schreibe

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

um:

(x - 3)^{3}

= (x - 3)^{7} - 9 (x - 3)^{3}

Klammere gleiche Terme aus

(x - 3)^{3} : (x - 3)^{3} ((x - 3)^{4} - 9)

= (x - 3)^{3} ((x - 3)^{4} - 9)

Faktorisiere

(x - 3)^{4} - 9 : ((x - 3)^{2} + 3) ((x - 3)^{2} - 3)

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

Vereinfache

(x - 3)^{3} ((x - 3)^{2} + 3) ((x - 3)^{2} - 3) : x (x - 3)^{3} (x - 6)

= x (x - 3)^{3} (x - 6)

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

= x (x - 6) (x - 3)^{\frac{3}{2}}

Beliebte Beispiele

\frac{x + 2}{x + 3} < 0

faktorisieren a^2-b^2+4a-4b

f a c t or a^{2} - b^{2} + 4 a - 4 b

r > 15 - 2 r

faktorisieren 2x^2-17x+8

f a c t or 2 x^{2} - 17 x + 8

9 y^{2} + 5 = - 76