First install the libraries using yum :
# sudo yum install sqlite-devel
# sudo yum install ruby-devel
Then, just install the sqlite3 gem :
sudo gem install sqlite3-ruby
That's it.
# sudo yum install sqlite-devel
# sudo yum install ruby-devel
sudo gem install sqlite3-ruby
tar -xvf ruby-1.9.2-p180.tar.gz
cd ruby-1.9.2-p180
./configure
make
make install
ruby -v
# cd rubygems-1.7.2
ruby setup.rb
mv /usr/bin/gem /usr/bin/bk_gem.old
ln -s /usr/local/bin/gem gem
gem -v 1.7.2
gem install rails
sudo mv /usr/bin/rake /usr/bin/rake.old
$ cd /usr/bin
$ sudo ln -s /usr/local/lib/ruby/gems/1.9.1/gems/rake-0.8.7/bin/rake rake