cd /usr/local/src
mkdir mod_pagespeed
cd mod_pagespeed
wget https://dl-ssl.google.com/dl/linux/direct/mod-pagespeed-stable_current_x86_64.rpm
rpm2cpio mod-pagespeed-stable_current_x86_64.rpm | cpio -idmv
cp /usr/local/src/mod_pagespeed/usr/lib64/httpd/modules/mod_pagespeed.so /usr/local/apache/modules/
cp /usr/local/src/mod_pagespeed/etc/httpd/conf.d/pagespeed.conf /usr/local/apache/conf/
chmod 755 /usr/local/apache/modules/mod_pagespeed.so
mkdir /var/mod_pagespeed/{cache,files} -p
chown nobody:nobody /var/mod_pagespeed/*
mod_pagespeed has a dependency that you’ll want to enable: mod_deflate (the httpd source directory (httpd-2.2.21) may vary depending on your install):