"It is better with a private health insurance."
Translation:Mit einer privaten Krankenversicherung ist es besser.
"Mit einer privaten Krankenversicherung ist es besser." is it right like this too: "Es ist besser mit einer privaten Krankenversicherung."? :o
"mit einXX privaten" is dative and "ein" is indefinite article... so the ending should be "en" instead of "er" (er is applied to feminine cases with no article). Someone can help me?
Duolingo's sentence is fine; your suggestion is not correct. I think you're mixing up article words (a, the, my,...) and adjectives (nice, small, private,...). They have different endings.
"Mit einer privaten Krankenversicherung":
einer: dative, feminine [dative because "mit" is always followed by the dative case; feminine because "Krankenversicherung" is feminine]
privaten: used after ein-word, dative, feminine [dative because of "mit", feminine because "Krankenversicherung" is feminine]
Article endings: http://german.about.com/library/blcase_sum.htm
Adjective endings: http://coerll.utexas.edu/gg/gr/index.html?si=adj
EDIT: At some point now long in the past, I incorrectly stated:
"Just to add to what Katherle said -- "einer" is not an article here, it is a possessive adjective. See here for a chart that includes possessive articles:"
EDIT: the chart is still useful though, even though I was wrong: http://www.lsa.umich.edu/german/hmr/grammatik/basic_chart.html
I don't understand how it is a possessive adjective. Can you (or someone else) clarify, or provide another link. Thank you in advance :)
@PatriciaJH @dnovinc : Like user dnovinc, I can't see how "einer" is a possessive adjective either. Checked the link and it's not even a possessive article. I don't think your advice is correct.
though the translation of "private" into "persönlich" isn't wrong in itself, this type of health insurance is just called "private Krankenversicherung", so that's the correct word for it ;) You wouldn't hear anyone call it "persönliche Krankenversicherung".