You resistor values are too low for use with a dying 9vdc battery. You should be using much higher resistance values, say two 10K ohm resistors. And when you take your voltage measurements read both the battery voltage while it's connected to the resistors as well as the Vo voltage reading. You should find that vo = 1/2 the battery voltage, any two equal size resistors will divide the applied voltage in half.
Lefty