In what situation,we should consider the balanced bridge when we calculate the equivalent capacity?
Term balanced bridge has been 150 years used for H-shaped circuit where the horizontal part has no voltage nor current because the left and right voltage dividers produce the same voltage. The idea was used originally in Wheatstone's resistance measurement bridge.

The same proportionality is true here; 4:6 = 6:9. If you consider 4uf, 6uF, 6uf and 9uF capacitors as impedances in an AC circuit you see their actions as two voltage dividers produce the same voltage. At all frequencies the omitted 5uF capacitor would have no current, it cannot be charged nor discharged. We can remove a current free part without affecting the rest of the circuit.

With different capacitor values general circuit calculation methods must be used. Y to delta transform can be used.