I'd like to do what most of us want to do; build muscle and lose fat. However it seems almost impossible to do both at the same time. I know that bcaa's are good for maintaining muscle while on a low carbohydrate diet. Is it possibly that you could gain muscle and lose fat, while on a high protein/low carbohydrate diet, if you used bcaa's?
You can, but its not optimal. Low carb is OK for fat loss, sub-optimal for muscle gain.
Personally I carb cycle so training days are relatively high carb - 150g or so. Non-training days are low carb, 50g of carbs.
Here are a few links to help:
Why it is bad:
Some links that say it works:
In general though you never want to be in an Atikins/Zero carb diet.
I recommend you check out google Timothy Ferris's Slow Carb Diet from the 4 Hour Body
It's a bit of the best of both worlds.
Also, in general, if you are eating low carb and attempting muscle gain, you want to make sure you get the correct ratio of protein and fat, just like other diets need correct P/F/C ratio.
Check out the IIFYM calculator, and it allows you to select lower carb diets like paleo or slow carb. Google IIFYM calculator.
How long have you been training? If you are relatively new to training you can gain muscle mass doing pretty much anything. But energy balance is far more important to whether you will build muscle than macro split. This is done by watching caloric intake. If you are consuming more than you're expending by 10-15% then you will build muscle and an optimum rate then any more will be mostly fat.
If you are consuming less then you are expending then you will lose fat and may build or lose muscle depending on how long you have been training for.
But to answer your question, definitely.