In a large bowl, whisk together the rice flour, tapioca starch, potato starch, xanthan gum, and salt until evenly combined. Make a well in the center.
Add the eggs and olive oil into the well. Use a fork to gradually pull the flour mixture into the eggs, stirring in a circular motion until a shaggy dough begins to form. If the dough is too dry and crumbly, add water one tablespoon at a time until it comes together.
Turn the dough out onto a surface lightly dusted with rice flour and knead for 3 to 4 minutes until smooth, pliable, and no longer sticky. Shape into a ball, wrap tightly in plastic wrap, and let it rest at room temperature for 20 minutes.
Divide the dough into 4 equal pieces. Working with one piece at a time and keeping the rest covered, flatten it slightly and feed it through a pasta machine starting at the widest setting. Fold the dough in half and pass it through again. Continue narrowing the setting one notch at a time until you reach your desired thickness, usually setting 5 or 6 for fettuccine.
Once the sheets are rolled, dust them generously with rice flour and cut into your desired shape, whether that is fettuccine, pappardelle, or lasagna sheets. Toss the cut pasta gently with a little extra rice flour to prevent sticking.
Bring a large pot of generously salted water to a rolling boil. Cook the fresh pasta for 2 to 3 minutes, until it floats and is tender but still has a slight chew. Drain and toss with your favorite sauce immediately.