If your opponent cannot do anything active, then don't rush the position; instead you should let him sit there, suffer, and beg you for a draw.
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[Event "rated untimed match"] [Site "?"] [Date "????.??.??"] [Round "?"] [White "Unknown"] [Black "Unknown86"] [Result "0-1"] [Annotator "David Hayes"] [BlackElo "0"] [FEN "6R1/3k3P/3p4/3r2B1/2pbp3/6P1/5P2/6K1 b - - 0 1"] [SetUp "1"] [TimeControl "0"] [WhiteElo "0"] 1... Rxg5 ( { Black can try: } 1... c3 2. Bf4 Rh5 3. Rg6 Bc5 4. Rg7+ Kc6 5. Kg2 c2 6. Bc1 d5 7. g4 Rh4 8. Kg3 Rh1 9. Kg2 Rh4 10. Kg3 Rh1 11. Kg2 { Draw by repetition of position. } ) 2. Rxg5 c3 3. Rd5 c2 4. Rxd4 c1=Q+ 5. Kg2 Qh6 6. Ra4 Kc6 { Black wins with a large material advantage. } 0-1