Q:

How can I track Google Analytics Across Multiple Domains in one account google?

I have installed Google Analytics on my website. The website is www.myhospitals.com. When the user clicks button A, it will track on Google Analytics. When the user clicks button B, it will also track on Google Analytics
But I want to add a new domain / new sub domain. The name is www.career.myhospitals.com
Can I add the domain on google analytics to one Google account? or I have to create a new account to track on that domain?

A:

You can use the same account for that...
Follow the steps

Click on the Admin at the bottom of the page

Now click on Add Property in the middle of the page.

Now select Web and complete the setup :-)

Hoping this would help you 

