With an HDMI splitter you can send the HDMI signal out of your computer, into the splitter, then send the two signals of the splitter to both your monitor and TV. The signal on the monitor and TV will be mirrored. The splitter should also accommodate audio.
You will generally not have a problem with weaker signal if using an HDMI splitter since it is all digital instead of analog.
I would definitely recommend splitting HDMI over VGA.