[tex]\dfrac{c^2-4}{6c^4+15c^3}\div\dfrac{c^2+4c+4}{12c^3+30c^2}=\dfrac{c^2-2^2}{3c^3(2c+5)}\div\dfrac{c^2+2(c)(2)+2^2}{6c^2(2c+5)}\\\\_{\text{use}\ a^2-b^2=(a-b)(a+b)\ \text{and}\ (a+b)^2=a^2+2ab+b^2}\\\\=\dfrac{(c-2)(c+2)}{3c^3(2c+5)}\cdot\dfrac{6c^2(2c+5)}{(c+2)^2}=\dfrac{(c-2)}{c}\cdot\dfrac{2}{(c+2)}=\boxed{\dfrac{2(c-2)}{c(c+2)}}[/tex]
