I just accidentally found out that I don't know how to win a pawnless endgame where I have 2 rooks and the opponent 1 rook. It should be a trivial win, but playing against the computer I didn't seem to make progress after 20 moves. At first I thought there should be a method where I can force exchanging one rook and convert the game into a basic checkmate K&R vs K. But try as I might, the computer didn't let me. Then I thought I would just checkmate him with my two rooks - he always interfered either with his king attacking one of my rooks or giving me check with his rook. My third idea was to checkmate him with one rook while the other rook was shielding me from his checks. This worked to a degree, but I couldn't get him down to the first rank.

So please can an someone either shoot me or show me how to win this? It must be trivial because it's covered neither in Silman's nor Dvoretsky's endgame book. 

Post a pgn-file of your trial and I will try it.

I didn't record my trial ... Anyway I would rather like to know the general idea/technique to win in such a position. Here's an example with Black to move and White's king already at the sidelines. I don't even know how to solve that! I'd greatly appreciate if you could help me out here. :)

Ok, for the above diagram, Fritz gives the following solution:

 

 

If anybody knows the general strategy/technique for these K+2R vs. K+R-endgames, please post! The posting above gave just the computer aided solution for one example and I can't see how this can be transfered to other such situations. 

It seems there's not much traffic here anyway - maybe I should post my question in one of the general forums?

You have to get your king in the action. He can walk a zigzag c4-d3-e4-f3 until he can force an exchanges of rooks.

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Can I always force an exchange of rooks in that type of endgame? What's with the checks he's able to give along the way?

There's a simple method. Hide your king behind behind one of the rooks. If both rooks are at the border approach the chess giving rook with your king till you attack the unprotected rook. Use the won move to activate the first rook.

Try to work out the rest for yourself. If you don't progress show your problem here with some lines.

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Thanks, indeed I had tried something like that before when I tried to checkmate him (my third idea in the original post), but it didn't work. Probably I had done something wrong at some point. I'll try again and if it doesn't work out I'll post again.

I annotated a pgn with some ideas:

Thanks friend, this was extremely helpful! It now seems to me that the correct method is the following:

Try to setup checkmate with the normal "ladder" technique, switching the rooks to the opposite side if he attack with his king. In addition if he checks your king with his rook, go hiding behind one of your own rooks. At one point he will be forced to intervene with his rook, leading to the desired "forced exchange" and conversion into a trivial K+R vs. K endgame.  

In retrospect, the main problem was how to bring about the desired forced exchange. The answer to this now seems to be "by just trying to mate him the usual way".

Is there still something else to consider?

@Bubatz: well done comment imo.