There are a few ways around this. The first is to raise the flash so that the shadows fall lower than the subject. This can help to minimise them.
The second is to have a flash that lights the background alone. That way you can overexpose it a stop or so and it will go completely white (if it's a white or grey backdrop, of course).
The second is to move your subject and flash away from the background. This works because light falls off pretty rapidly with distance (if you double the distance between the light and whatever the light is hitting, you need four times as much light to make it look the same). Increasing the distance between the flash and the background means that by the time the light from the flash reaches the background, it is less intense, so the contrast between shadow and light will be lower.
probably the best solution would be to increase the distance, and adjust your exposure so that the background is under-exposed. Then you can add a background light to bring the background to the brightness that you want, and it should also remove any shadows.