Answer:
[tex]\dfrac{34(a+2)}{23(a-13)}[/tex]
Step-by-step explanation:
Realize that dividing by a fraction is the same as multiplying by its inverse. Then factor the expressions and cancel common factors from numerator and denominator.
[tex]\displaystyle\frac{\left(\frac{2(a^2+5a+6)}{5(a^2-169)}\right)}{\left(\frac{23(a+3)}{85(a+13)}\right)}=\frac{2(a^2+5a+6)}{5(a^2-169)}\cdot\frac{85(a+13)}{23(a+3)}\\\\=\frac{2\cdot 5\cdot 17(a+13)(a+3)(a+2)}{5\cdot 23(a+13)(a+3)(a-13)}=\frac{34(a+2)}{23(a-13)}[/tex]
