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The voltage divider is for the serial Arduino TX to BT RX connection.

The actual Bluetooth module (the small daughter-board) is a 3.3v device. Most HC-0xs have regulators on the breakout board to bring down vcc to 3.3v (this is why they canaccept up to 6v) but they do not convert the TX or RX pins which are still 3.3v. The voltage divider steps down the Arduino TX 5v pin to around 3.3v. A 5v Arduino sees 3.3v as HIGH so there is no need to upstep the 3.3v BT TX pin and it can be connected directly to the Arduino RX pin.