How would you prove mathematically that the GDP per capita growth rate (from time t to t+1) can written as the sum of GDP per worker growth rate from time t to t+1 and the growth rate of the working age fraction of the population from time t to t+1 such that employment rate remains constant?

note: Given that GDP per capita = (GDP per worker)(employment rate)(working age fraction of population) since GDP/total population = (GDP/total employed workers)(employed workers/working age population)(working age population/total population)