A summary of the rules can be found here. This is slightly different from virmaior's.
1. P(x) v Q(x) hyp
2. ~P(x) hyp
3. | P(x) hyp
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4. | ⊥ ⊥ Intro 2, 3
5. | Q(x) ⊥ Elim, 4
6. | Q(x) hyp
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7. | Q(x) Reit 6
8. Q(x) v Elim, 1, 3-5, 6-7