When you brush your teeth, it's to remove any plaque that has accumulated in a short period of time and to clean other soft debris from them... it's not to remove any hard deposits (calculus/tartar), that's what professional cleanings are for.

A soft-bristled brush is recommended so as to not harm the gums, in fact it's suggested to actually massage them during brushing. A hard-bristled brush can cause what's known as 'toothbrush abrasion', which occurs when brushing too hard in the same direction day after day.

Start fresh: get yourself a new brush, and try being more gentle on your teeth and gums. Brush in a 'c' motion, holding the brush at a 45 degree angle to your gums, and use minimal pressure. Ideally a toothbrush should be replaced at least every three months; this should prevent the 'frayed' condition of the brush as well.

~Hope this helped!