I need a hint regarding the following problem in field extensions.

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Let $L/K$ be a field extension. Let $t$ be a transcendental element over the field $K$. Find the minimal polynomial of $t$ over $K(\frac{t^3}{2t+1})$

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Hint: If $s = t^3/(2t+1)$, then $t^3 - (2t+1)s = 0$.
Is that minimal?