(x^8-x^2)/(x^4-x^2)=9

Lösung

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} = 9

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

Schritte zur Lösung

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} = 9

Vereinfache

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} : x^{4} + x^{2} + 1

x^{4} + x^{2} + 1 = 9

Löse

x^{4} + x^{2} + 1 = 9 : x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 1, x = - 1, x = 0

Kombine die undefinierten Punkte mit den Lösungen:

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

\frac{6}{x - 3} - 6 = - 12

so l v e f or t, \frac{r}{t} = d + 10

\frac{x - 1}{x + 3} + \frac{x - 2}{x + 1} = 1

\frac{3}{x - 4} = \frac{x - 5}{x}

x - \frac{2}{x} = - 1