Well, the problem with your script is that you never retrieve the values from the SQL query; [man]mysql_query/man returns a resource to the query. You need to actually retrieve data using functions such as [man]mysql_result/man, [man]mysql_fetch_assoc/man, etc.
There's no need, however, for two separate queries (and especially not for two separate connections!) to accomplish this. Try something like this:
SELECT c.tax2 + n.Tax AS tax_sum
FROM invoice.clients c, new_sql.news n
I don't quite understand your DB schema, however. Are you trying to add all of the values for the "tax2" column, and add all of the values in the "Tax" column, and then add those two sums together? If so, you'd want:
SELECT SUM(c.tax2) + SUM(n.Tax) AS tax_sum
FROM invoice.clients c, new_sql.news n
If that's not what you want (or even if it is), you may want to rethink your database design. If these two tables hold related data, why are they in separate databases?