5x+21+178 / (x-7)

How do I solve for domain and range on this equation?

The domain is easiest. You simply need to find the fractions, and exclude any X that makes the denominator zero. So in this case, your domain is everything except X=7.

For range, you are trying to find out what are the possible answers. Usually the best way to do this is to try x=infinity, and x=negative infinity, which here gives you answers of infinity and negative infinity. Since the function is almost continuous, I think your range is any real number.