1. Easier access to firearms, and other suicide methods. Gun ownership in rural areas is higher than in cities, and I'd wager that gun suicides by gun are a lot more likely to succeed than other methods (e.g., jumping off a building.)

2. People in rural areas may socialize less, and may have less of a support network. I live in New York, and if I want to see my friends after work, it's an extra 5 minutes on the train for us, and an easy way to get home after having a few rounds at the bar. If I were back in Dallas, it might be 45 minutes out of my way in traffic, and it would be much more difficult to get home and then back to work again if I couldn't drive my car home. In a more isolated area, your friends might live two hours from you, or two states over.

3. Some suicide attempts are actually cries for help, and in a dense city, more people may notice that cry.

1) further distance from hospitals mean more people die.

2) great access to means and methods - guns, vet meds, etc.

3) more high risk jobs (farmers, vets, and rural workers are high risk jobs (because means and methods, and also because economic uncertainty)

4) more stigma around suicide and mental health.