@stephen J Bauer:
"So not only are some scientists providing analogies that black holes eat, but now some other scientists would like us to believe that some black holes even burp, or belch out matter."
The words "belching" and "indigestion" are incredibly stupid ones to use in this situation, and does create confusion (or maybe the writer didn't understand the concept).
Supermassive blackholes are surrounded by a swirling disk of dust and gas called an accretion disk. This disk gets hotter as it gets close to the black holes event horizon (the distance from the gravitational center where the escape velocity equals the speed of light). The temperature of the accretion disk close to the event horizon is many times hotter than the surface of stars.
If a star strays close to the black hole, it can get shredded and suddenly a glut of material hits the accretion disk. When this material collides with the super heated disk, part of it erupts outwards at close to the speed of light, in narrow jets perpendicular to the plane of the accretion disk. These jets then collide with gas and dust, producing x-rays and radio waves.
So, no matter comes out from the event horizon of the black hole. From our current understanding of physics, nothing can. The matter, in this case, is blasted out from the accretion disk.