Question 982179
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).


{{{(5/a+1)+8/(4/a+1)+3}}}
Simplest denominator is a.


{{{5/a+a/a+8/(4/a+a/a)+3a/a}}}


{{{(5+a)/a+8/((4+a)/a)+3a/a}}}


{{{(5+4a)/a+8/((4+a)/a)}}}


{{{(5+4a)/a+8a/(4+a)}}}
Misidentified the actual simplest common denominator, but what used up to now helped.  The simplest denominator for common purposes is a(a+4).


{{{((5+4a)/a)((a+4)/(a+4))+(8a/(4+a))(a/a)}}}


{{{((5+4a)(a+4)+8a^2)/(a(a+4))}}}


{{{(5a+16a+20+4a^2+8a^2)/(a(a+4))}}}


{{{highlight((12a^2+21a+20)(a^2+4a))}}}