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I believe it was a trilogy. It was set in a universe where dragons are pitted in fights against each other for humans' benefit, and the main character was a stableboy who helped to take care of dragons. I remember early on in the first book he gets injured by a dragon, and a woman who is taking care of his wounds comments on how otherwise unscarred his back is, which embarrasses him.
At some point he discovers that he has an empathic connection with dragons (!?) and everything goes down south when a dragon he'd been helping his mentor figure prepare gets injured ("hamstrung") and has to be put down. As the mentor administers a mercy killing to the dragon, the main character was visualizing a candle being snuffed out.
One of the novels ended with the main character and his female traveling companion both developing an empathic/psychic bond with their dragons and with each other; when their dragons communicate with them, they hear/see/feel it in rainbows.
I remember discovering it in a middle school library; I believe it's young adult. It wouldn't have been published any later than 2005