faktorisieren (t-3)^{7/2}-(t-3)^{3/2}

Lösung

faktorisieren

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

(t - 2) (t - 3 + 1) (t - 3 - 1) (t - 3)^{\frac{3}{2}}

Schritte zur Lösung

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

Schreibe

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

um:

(t - 3)^{7}

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

Schreibe

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

um:

(t - 3)^{3}

= (t - 3)^{7} - (t - 3)^{3}

Klammere gleiche Terme aus

(t - 3)^{3} : (t - 3)^{3} ((t - 3)^{4} - 1)

= (t - 3)^{3} ((t - 3)^{4} - 1)

Faktorisiere

(t - 3)^{4} - 1 : ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1)

= (t - 3)^{3} ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1)

Vereinfache

(t - 3)^{3} ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1) : (t - 3)^{3} (t - 2) (t - 3 + 1) (t - 3 - 1)

= (t - 3)^{3} (t - 2) (t - 3 + 1) (t - 3 - 1)

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

= (t - 2) (t - 3 + 1) (t - 3 - 1) (t - 3)^{\frac{3}{2}}

(p + 1)^{2} = 11 (p + 1) - 30

s im pl i f y 2^{n} + 2^{n}

- 1 - j > 1

4 x^{2} - 36 x = - 93

lo g_{8} (3 x + 7) < lo g_{8} (7 x + 4)