faktorisieren (x-7)^{7/2}-49(x-7)^{3/2}

Lösung

faktorisieren

(x - 7)^{\frac{7}{2}} - 49 (x - 7)^{\frac{3}{2}}

x (x - 14) (x - 7)^{\frac{3}{2}}

Schritte zur Lösung

(x - 7)^{\frac{7}{2}} - 49 (x - 7)^{\frac{3}{2}}

Schreibe

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

um:

(x - 7)^{7}

= (x - 7)^{7} - 49 (x - 7)^{\frac{3}{2}}

Schreibe

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

um:

(x - 7)^{3}

= (x - 7)^{7} - 49 (x - 7)^{3}

Klammere gleiche Terme aus

(x - 7)^{3} : (x - 7)^{3} ((x - 7)^{4} - 49)

= (x - 7)^{3} ((x - 7)^{4} - 49)

Faktorisiere

(x - 7)^{4} - 49 : ((x - 7)^{2} + 7) ((x - 7)^{2} - 7)

= (x - 7)^{3} ((x - 7)^{2} + 7) ((x - 7)^{2} - 7)

Vereinfache

(x - 7)^{3} ((x - 7)^{2} + 7) ((x - 7)^{2} - 7) : x (x - 7)^{3} (x - 14)

= x (x - 7)^{3} (x - 14)

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

= x (x - 14) (x - 7)^{\frac{3}{2}}

s im pl i f y 4 81 x^{5} y^{4} \cdot 4 32 x^{3} y

\frac{a}{- 8} + 15 > 23

s im pl i f y 232

s im pl i f y 25 + 5

20 < 4 x