A cynic would attribute the disparity (and the failures to gentrify) to indifference or inattention, (or worse) disdaining neglect or ignoring, by the politicians and rich of the poor in the poor areas.
I exemplify with cities whose disparities I have witnessed, followed by links to the maps overlaying location with income, but I exclude downtown areas which always appear rich:
New York: (Lower) Manhattan vs. The Bronx and Brooklyn (e.g. Bedford-Stuyvesant, Bushwick)
<Google search: 1, 2>
London (Boroughs): Hammersmith & Fulham, Kensington & Chelsea, Westminster
vs. Hackney, Tower Hamlets, and the southern boroughs like Lewisham, Croydon.
<Google search: 3, 4, 5>
Toronto: Midtown (along Yonge St. subway line, like Lawrence Park) vs. Jane & Finch, Rexdale
<Google search: 6>
Vancouver: West & North Vancouver, West Side, South Vancouver vs. Downtown East Side, Surrey
<Google search: the Vancouver Sun has many maps.>