Learn German: Der Trainer hofft, dass das neue Mitglied mitmacht. - The trainer hopes that the new member joins in.

This is the main rule for this lesson! Normally, the separable verb mitmachen splits up, like in Er macht mit (He joins in). However, the word dass creates a subordinate clause, which pushes the conjugated verb to the very end of the sentence. When a separable verb is pushed to the end like this, the prefix (mit) and the verb (macht) recombine into a single word: mitmacht.

Why does the adjective in das neue Mitglied end in just -e instead of -es?

Mitglied is a neuter noun (das Mitglied). Because the definite article das is already there to show us the neuter gender and nominative case, the adjective neu only needs the weak ending, which is just -e.

How does the word mitmachen translate literally?

It translates roughly to 'to make with' or 'to do with' (from mit and machen), but it is the standard, everyday German verb for 'to participate', 'to join in', or 'to take part' in an activity.

Is the comma before dass optional?

No, it is mandatory. Unlike in English where a comma before 'that' is usually skipped, German strictly requires a comma to separate the main clause (Der Trainer hofft) from the subordinate clause.