<PRE><B>Question 17594</B>
Do you mean {{{ (a+6)/(a+2) + 16/(a^2-4) }}}??  If so, then the first step in adding fractions is to factor the denominators so as to find the LCD.


{{{ (a+6)/(a+2) + 16/((a-2)(a+2)) }}}  and the LCD = (a-2)(a+2).


In order to get the LCD in the first fraction, you already have the (a+2) factor, but you will need to multiply numerator and denominator of this first fraction by (a-2).  The second fraction already has the LCD, so leave it alone.


{{{ ((a+6)/(a+2))*((a-2)/(a-2)) + 16/((a-2)(a+2)) }}}  


Now you have an LCD of (a-2)(a+2), and this becomes THE denominator of the fraction:

{{{ (______________________)/((a-2)*(a+2)) }}}


Now, just add numerators together as follows:

{{{ ( a^2 +4a-12 + 16)/((a-2)*(a+2)) }}}


Simplify:  {{{(a^2 + 4a +4)/((a-2)(a+2))}}}


The numerator DOES factor, so you must factor the numerator in order to reduce the fraction.

{{{((a+2)*(a+2))/((a-2)(a+2))}}}


Divide out the (a+2) factor in the denominator with one of the numerator factors: 

{{{ (a+2)/(a-2) }}}  FINAL ANSWER!!


R^2 at SCC</PRE>