Alex spricht auf einer Party eine fesche Brünette an.
Alex speaks to a chic brunette at a party.

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A separable prefix verb is one in which the stem is conjugated, while the prefix appears at the end of the main clause.  

Alex mag auf einer Party eine fesche Brünette ansprechen.
Alex may speak to a chic brunette at a party.

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When an auxilary verb or modal is present, the separable prefix verb is found at the end of the sentence or clause in the infinitive form.  

.., weil Alex auf einer Party eine fesche Brünette anspricht.
.., weil Alex auf einer Party eine fesche Brünette ansprechen mag.

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In subordinate clauses, the conjugated form of the verb appears at the end.