Which Nikon camera for a DX lens?

I have a Nikon D5100, with 3 DX lenses, but I would like to upgrade it to a faster shutter speed frame camera also with more AF points, ( 51 for example, as the D5100 got 11 only) I was interested with the Nikon D800, but it is FX, is anyone could tell me if my DX lenses will work on it, or guide me to a Nikon DX camera?

The D800 uses DX lenses perfectly well.

I have a number of DX lenses which I use on both my D800 or D3.

The other camera you may want to consider is the new Nikon D7100.

Visit the Nikon website and look at the features of both cameras and decide which you want to buy. If you pick the D7100, you will have some money left for a fourth lens

The logical choice is the Nikon D7100 which is a Dx camera and has 51 focus points - the same focus circuits as used in the D800.

You can use the D800 with your Dx lenses, but with reduced resolution (the D800 goes into Dx mode).