Learn French: Tu amélioreras tes performances à condition de t'entraîner. - You will improve your performance provided you train.

You use à condition de followed by an infinitive when the subject is the same in both parts of the sentence. Here, tu is doing both the improving and the training. If the subjects were different, you would need to use à condition que followed by the subjunctive.

If the verb is in the infinitive, why is it t'entraîner and not s'entraîner?

With reflexive verbs, the reflexive pronoun always has to agree with the person performing the action, even when the verb itself is left in the infinitive. Since the implied subject doing the training is tu, the pronoun must be te (which contracts to t' before a vowel).

Why is tes performances plural in French but translated as the singular "performance" in English?

In French, une performance often refers to a single specific feat, race result, or show. To talk about someone's overall capability, execution, or ongoing track record, French prefers the plural les performances. English, on the other hand, usually treats "performance" as an uncountable singular noun in this context.