IS THIS POSSIBLE? How to have to copies of a blog???

Right I am pretty new to wordpress but will try my best to explain what I want to do.

I have a wordpress site with a home, about, portfolio, blog and contact pages. call it domainA.com

Now I also have domainB.com that currently just forwards to domainA.com.

What I want, is for domainB.com to only have/show a copy of domainA.com’s blog page.

So domainA.com is a full site with a blog on it.

domainB.com just shows a copy of domainA.com’s blog

I hope that makes sense. If your going to ask why, its basically because I have a blog for my business but I want to double it up as a personal blog. I want to direct my friends to one place and businesses to another.

Thank you in advance