Q: Help! Can't mirror 2009 Macbook Pro to TV via Apple TV3

Mirroring requires a Mac from 2011 or later. You would need to use a 3rd party program like Airparrot, results vary so use the trial first

You need an Apple TV to use AirPlay mirroring regardless. It's your Mac that is too old, mirroring requires the newer chip to do video encoding. As I said, you could use a 3rd party program like Airparrot, however as it is done through software and relying on the CPU results will vary.

Here's a link to the minimum requirements for AirPlay Use AirPlay to display video from your Mac on an HDTV - Apple Support

Minimum requirements if your Mac and Apple TV are on the same network:

• Apple TV (2nd generation or later) with the latest Apple TV software
• For mirroring your display or extending your desktop, any of the following Mac computers with OS X Mountain Lion v10.8 or later:
  
  • iMac (Mid 2011 or later)
  • Mac mini (Mid 2011 or later)
  • MacBook (Early 2015 or later)
  • MacBook Air (Mid 2011 or later)
  • MacBook Pro (Early 2011 or later)
  • Mac Pro (Late 2013 or later)

Minimum requirements for peer-to-peer AirPlay, which lets visitors quickly and easily connect their Mac or iOS device to your Apple TV without gaining passwords and connecting to the Wi-Fi network:

• Apple TV (3rd generation rev A, model A1469 or later) with the latest Apple TV software
• A Mac (2012 or later) with OS X Yosemite v10.10 or later