Using a Nikon D3000 - why are my photos overexposed using shutter priority mode?

I photograph people in nightclubs and bars (so in low light conditions), when i use shutter priority mode and try to lengthen the shutter speed for bright backgrounds the people are really over exposed, is this because of the aperture? Shouldn't the camera automatically change the aperture so that your photo is exposed correctly if in shutter priority mode?

Added (1). So then how do i get bright backgrounds without overexposed people? Do i need an external flash?

If you lengthen exposure to make the background lighter, the entire image will become brighter. The camera did pick the correct aperture for a correct exposure of the dark background. Since the people in the foreground were lighter than the background, they became overexposed.

You really need to learn the basics of photography…

There's NOTHING wrong with your camera

I guess you never look at what the light meter is telling you.

Just because the camera will take the shot, does NOT mean that the exposure it going to be correct.

You need to monitor your cameras light meter to assure proper exposure.

The lens can only work within the range of the lens apertures it has. If the correct exposure needs a smaller aperture, then you need to reduce your cameras ISO setting or increase the shutter speed.

This is how that works

http://camerasim.com/camera-simulator/

"so then how do i get bright backgrounds without overexposed people? Do i need an external flash?"

If the light ratio is extreme, you can't get bright backgrounds without overexposing the people

After decrypting your English I can only guess that you want to shoot bright background portraits in low light. Lets first start by telling you what you need to do, using full manual mode you should select a large aperture, and a slow shutter speed of around 1/15 or 1/30, and an ISO of 400-800. Use your pop up flash with a flash exposure compensation of -3EV this will provide the freeze motion. This is my tried and tested recipe for working ultra low light conditions.

Now what you're doing wrong could be a whole host of things:

1) Matrix metering is getting thrown off by dark background over compensating. Use spot or partial metering, and exposure compensation to make sure the people are correctly exposed.

2) Your shutter speed may be too slow and your lens can't stop down enough (keep an eye on your light meter and your aperture values. If it's blinking at f/22 you need to speed up.

3) Flash metering may be getting confused. If you're using TTL flash, your camera will prefire the flash to determine the amount of reflected light, where there's a dark background only a small amount of reflected light is returned, and this can throw the flash off and cause it to be fired with too much power. You may need to dial it down using FEC.

4) You're simply standing too close when using the flash. It's difficult in a cramped club to space yourself out, but if you're shooting right in someone's face the flash exposure needs to be done very carefully.

To address points 3 and 4 properly a flashgun will help greatly as it gives you the flexibility to bounce light or use diffusers like an Omnibounce, or a Fongsphere.