I have a simple static class with a few methods in it. Each of those methods open a SqlConnection, query the database and close the connection. This way, I am sure that I always close the connection to the database, but on the other hand, I don't like to always open and close connection. Below is an example of what my methods look like.

public static void AddSomething(string something)
{
    using (SqlConnection connection = new SqlConnection("..."))
    {
        connection.Open();
        // ...
        connection.Close();
    }
}

Considering that the methods are inside a static class, should I have a static member containing a single SqlConnection? How and when should I drop it? What are the best practices?