I think that the two situations are not linked. Generally speaking, the best way out of poverty is education focussed on equipping people will the skills necessary to secure well-paid jobs in the modern work. This requires investment by governments in the education of their citizens PLUS hard work and focus by learners. The old adage that you can lead a horse to water but you can't make it drink is true - too many kids here in the U.K. do not appreciate how lucky they are to have access to free education up to the age of 18. And too many parents do not seem to know that the best thing they can do for their children is to encourage them to work hard in school. I am from a working class background. My mother taught me and my two sisters to read before we started school. We were all encouraged to enjoy learning and we all eventually went to university, secured good jobs, and continued to learn and acquire new skills.This was in the days before the introduction of university tuition fees. This year there has been a decline in university applications by working class kids because they know that by the time they have earned their degrees they will have amassed huge student loan debts.
The rich get richer for a number of reasons. High earners have large sums of disposable income which they are able to save and invest. If they have invested wisely, the income from their investments increases year on year. Some people have vast inherited wealth and will never need to work. Some people have acquired wealth through shady deals or corrupt governments.
The only way to redress the balance between wealth and poverty is by taxing the rich and using the tax revenue to improve educational opportunities and to invest in job creation.