Do livebearers do well with plants in the tank when they give birth or are they better off without them?

It doesn't really matter for the adult that has given birth, but it could mean life or death for the fry. The plants give the fry a place to hide and lessen the likelihood that they'll be eaten by other fish in the tank.

Well said Derek.  Many livebearers will tend to eat their fry and plants offer a great place for them to hide.  Also, planted tanks can be very beautiful and very rewarding if you enjoy that type of work.  I have a number of tanks and at least four of them are planted with live plants.  The fish seem to enjoy playing amongst them and I enjoy learning and working with them.

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I Luv Guppies

If you have a planted tank a lot of times tiny organisms will live on the plants and provide a food source for the fry.  Java moss often works well for this.