Does it invalidate prayer to read it fast?
If reading fast makes you not articulating the letters properly and/or changes the meaning of the verses that you are reciting, then your prayer will be invalid. If the meaning is not changed, then the prayer is valid; however, you don't get any reward from that prayer except for the amount of time you were actually having Khushu' خشوع (concentration) in that prayer.
Also, do your best to get rid of that habit because that, praying fast, is one of the attributes of the hypocrites (Munafiqeen). The Prophet (PBUH) said (the hadith is in Sahih Muslim):
That is the prayer of the munafiq. He waits until the sun is between
the horns of the Shaytan (just before sunset), then he pecks four
times, and he does not remember Allah, except a little.
Allah knows best!