Can I use an HDMI splitter to operate my PS3/PS4 on two tv's in different rooms?

Hey Guys, I'm hoping you can offer some assistance. We have 2 tv's in our home and until recently had a PS3 on each that worked as our media center. My hubs upgraded to a PS4 though and got rid of the other PS3. Then we discovered that the PS4 is actually very limited because it does not have DLNA streaming. We have the PS4 in the living room and on the exact opposite side of the wall is where we have our bedroom tv. So we were wondering can we simply run an hdmi splitter through the wall and be able to switch between PS3 or 4 depending on what we are doing (gaming or streaming from media center)? Thanks!