To take care of ourselves we must

we must keep up with our personal hygiene.

Explanation:

We have to keep up with our personal hygiene so we don't smell bad or look bad

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.  

whats the question you didnt post a question

explanation: