Problem
You are trying to install the mysql gem in Mandriva, but it fails with error messages:

ERROR:  Error installing mysql:
ERROR: Failed to build gem native extension...
checking for mysql_query() in -lmysclient... no ....

Solution
After searching in google, with solutions about providing different options (– –with-mysql-config, ..etc), even trying different combinations for providing the client library path, the configuration file, or the header file path, was still faced with the same error installing the mysql gem.
As the Mandriva installation was quite new, it turns out to be a couple of missing packages.
So try:

urpmi gcc
urpmi make

and run:

gem install mysql

again.

It should work out ok install the gem and output:

Building native extensions. This could take a while...
Successfully installed mysql-2.7
1 gem installed