Pay attention to the arithmetic.
If your load takes 0.5A @ 9V
R = 9V / 0.5A = 18Ω
Your load represents a resistor of 18Ω.
Your voltage divider becomes 6Ω + [18Ω] where the [18Ω] is already in the load and is not an additional resistor.
This is a far cry from your 10KΩ + 30KΩ.
They both present a 1:3 ratio but the current through the 10KΩ resistor is too low to power your project or even do any damage.
Hence nothing was damaged.
The recommended solution is to get a 7809 regulator or a buck DC-DC converter.
If you are driving a string of LEDs that take 0.5A then what you need is a constant 0.5A supply, not a constant voltage supply.
Tell us what you are trying to do.
If your load takes 0.5A @ 9V
R = 9V / 0.5A = 18Ω
Your load represents a resistor of 18Ω.
Your voltage divider becomes 6Ω + [18Ω] where the [18Ω] is already in the load and is not an additional resistor.
This is a far cry from your 10KΩ + 30KΩ.
They both present a 1:3 ratio but the current through the 10KΩ resistor is too low to power your project or even do any damage.
Hence nothing was damaged.
The recommended solution is to get a 7809 regulator or a buck DC-DC converter.
If you are driving a string of LEDs that take 0.5A then what you need is a constant 0.5A supply, not a constant voltage supply.
Tell us what you are trying to do.