"I live in the suburbs of Baghdad."
Translation:أَسْكُن في ضَواحي بَغْداد.
The suburbs of Baghdad form what's called an iDaafa or status constructus. The first noun will never have the definite article (as it's "explained" by the following word) and the second word will always be in the genitive case - have a kasra vowel "i" at the end. If the second word has the article, the whole iDaafa is considered definite. Also, the case of the first word determines the case for the whole iDaafa.