You can put this solution on YOUR website! If you mean (5/a+1)+8/(4/a+1)+3 exactly as you give, then to carry out the arithmetic, do what you already learned (even if you mean a different given expression, still of the rational kind).
Simplest denominator is a.
Misidentified the actual simplest common denominator, but what used up to now helped. The simplest denominator for common purposes is a(a+4).