Frodo also needed Gollum. Before he betrayed them, he served as their guide. Frodo says that they never would have made it through the marshes without Gollum. Gandalf also says that Gollum still has a part to play.
I think a lot of Frodo's compassion is because Gollum was willing to help them. He makes a statement or thought along the lines of "The servant has the right to expect loyalty from the master" when he is debating whether to let Faramir's men shoot Gollum for coming to thier hideout.
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