Question

$( frac{6a+c}{ a^{2}-6ac }+ frac{6a-c}{ a^{2}+6ac})* frac{ a^{2}-36 c^{2} }{ a^{2}+ c^{2} }$

Answer 1

$( frac{6a+c}{ a^{2}-6ac }+ frac{6a-c}{ a^{2}+6ac})* frac{ a^{2}-36 c^{2} }{ a^{2}+ c^{2} } =( frac{6a+c}{ a(a-6c) }+ frac{6a-c}{ a(a+6c)})* frac{ a^{2}-36 c^{2} }{ a^{2}+ c^{2} } =\\=frac{12(a^2+c^2)}{a(a^2-36c^2)}*frac{ a^{2}-36 c^{2} }{ a^{2}+ c^{2} }=frac{12}{a}$