This is a serious question. I have decided that I would put all my effort and resources into the front lawn of my house. Because the dog rules the roost in the back yard, I won't do anything but mow the back. But a strange thing has happened. The area where he does "his business" is lust, thick and weed free, while the rest of the grass is thin and covered with weeds. I have heard that pet urine can be damaging to a lawn, but that's not what i'm seeing in my back yard.
Interesting! "Aged" urine is actually a good fertilizer. Usually that means leaving the urine sit for a while, at least a couple weeks, before applying it. Aged manure is also a good fertilizer, but fresh manure straight out of the animal usually contains too much nitrogen and will give plants a nitrogen burn. Not sure what you're seeing! Consider other factors, like sunlight. And maybe get a soil test and test both locations. Or, maybe your grass is particularly hearty in the backyard and doesn't mind all of the raw fertilizer it's getting
Fresh urine contains urea which becomes ammonia which in turn is converted into nutritious nitrates by bacteria in soil. Essential potassium and phosphorus are also present in urine. Usually the standard advice is to dilute fresh urine at a ratio of about 1 part urine to 8 parts water (preferably "grey water"). Apparently undiluted urine can be used but the salt content can damage plants (Which is why neat urine can also be used as a weed killer). My advice is to have your dog pee in the front but dilute it with a watering can if it's not raining. Diluted human urine is just as effective at giving plants essential nutrients. So maybe you could accompany Rex.