PCI = Y(Income)/P(population) PCI growth rate is (change in PCI)/PCI How is this equal to the difference between income growth rate and population growth rate? In other words how is (∆(Y/P))/(Y/P) = (∆Y/Y) - (∆P/P) ?

We know: $PCI = \frac{Y(Income)}{P(population)}$ and that $PCI$ growth rate is $\frac{\Delta PCI}{PCI}$.

How is this equal to the difference between income growth rate and population growth rate?

In other words how is $\left(\frac{∆\frac{Y}{P}}{\frac{Y}P}\right) = (∆Y/Y) - (∆P/P)$ ?

PCI = Y(Income)/P(population) PCI growth rate is (change in PCI)/PCI How is this equal to the difference between income growth rate and population growth rate?

PCI = Y(Income)/P(population) PCI growth rate is (change in PCI)/PCI How is this equal to the difference between income growth rate and population growth rate? In other words how is (∆(Y/P))/(Y/P) = (∆Y/Y) - (∆P/P) ?