Implant versus crown

[zadam123]

I was told this tooth is hopeless. About 3 weeks ago it started to hurt for about a day after taking antibiotics the pain kind went away. I've been to the dentist they told me the truth is hopeless and the fact that it don't hurt anymore doesn't mean anything and I need to have it pulled. They think it's fractured but they said cannot tell on x-rays. Here's my question does it really need to be pulled if it really doesn't hurt anymore? And I was quoted about 4, 000 for the extraction a bone graft with membrane implant and crown. This is not covered by my insurance. Is this a normal amount? My other option would be a bridge which I would be covered for through insurance but the dentist is trying to talk me out of this and push the implant. He says the bridge may cause damage to the other two teeth when doing a root canal to attach the bridge and might be more work. Is this really true? Also what is the real difference between a bridge and an implant? Is a bridge really that bad? Thanks