Rook and Two Pawns vs Rook and One: The e6 Wedge

Watch the method: press play to see the winning idea run, or step through it move by move.

With all the pawns on one wing, an extra pawn wins only when it does real work. Here the pawn on e6 is a wedge: it strips the black king of the squares it would use to blockade, and that is what turns rook and two pawns against rook and one into a win.

The king invades, the rook stays home. Your rook on e5 guards the e-pawn from the side, so the king marches in with Kg6 and takes g7. The black rook can only check from behind, and trading rooks is fine, though not because the wedge survives: after Rxg5+ Kxg5 Black takes it back with Kxe6. The pawn ending is won all the same, and by exactly one move, Kg6.

Shelter, then shut the door. After winning g7, the king hides on h6 in front of its own pawn, where the checks stop. Then Rg5 blocks the file for good and the h-pawn promotes.

In this drill the defender will check from behind and try to trade rooks: answer the g-file check with Rg5. The trade is welcome, but not for the reason it looks: after Rxg5+ Kxg5 Black answers Kxe6 and the wedge is gone. The pawn ending is won anyway, and only by Kg6, which goes after the g-pawn and then runs the h-pawn.