Rationale Parametrisierung/Gleichung/3/Aufgabe

Bestimme für die Abbildung

{\mathbb {A} }_{K}^{1}\setminus \{0\}\longrightarrow {\mathbb {A} }_{K}^{2},\,t\longmapsto \left({\frac {t^{2}+t+1}{t^{2}}},\,{\frac {t-1}{t^{2}}}\right),

eine algebraische Gleichung der Bildkurve.

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