faktorisieren x^{(-9)/2}+2x^{-7/2}+x^{(-5)/2}

Lösung

faktorisieren

x^{\frac{- 9}{2}} + 2 x^{- \frac{7}{2}} + x^{\frac{- 5}{2}}

\frac{( x + 1 ) ^{2}}{x ^{\frac{9}{2}}}

Schritte zur Lösung

x^{\frac{- 9}{2}} + 2 x^{- \frac{7}{2}} + x^{\frac{- 5}{2}}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

x^{- \frac{7}{2}} = x^{1 + \frac{- 9}{2}} = x^{1} x^{\frac{- 9}{2}}, x^{\frac{- 5}{2}} = x^{2 + \frac{- 9}{2}} = x^{2} x^{\frac{- 9}{2}}

= x^{\frac{- 9}{2}} + 2 x^{1} x^{\frac{- 9}{2}} + x^{2} x^{\frac{- 9}{2}}

Klammere gleiche Terme aus

x^{\frac{- 9}{2}}

= x^{\frac{- 9}{2}} (1 + 2 x + x^{2})

Faktorisiere

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

= x^{\frac{- 9}{2}} (x + 1)^{2}

Fasse zusammen

= \frac{( x + 1 ) ^{2}}{x ^{\frac{9}{2}}}

Y = (0)^{2}

s im pl i f y \frac{- 6}{- 7}

s im pl i f y e^{i \cdot \frac{π}{2}}

f a c t or r^{3} - 125

f a c t or - 16 t^{2} + 1444