(a-2)/(4a^2+16a+16) : (a/(2a-4) - (a^2+4)/(2a^2-8) - 2/(a^2+2a))

Question

(a-2)/(4a^2+16a+16) : (a/(2a-4) - (a^2+4)/(2a^2-8) - 2/(a^2+2a))

Answer 1

(a-2)/(4a^2+16a+16) : [a/(2a-4)-(a^2+4)/(2a^2-8)-2/(a^2+2a)] =
= (a-2)/(4(a+2)^2) : [a/(2(a-2))-(a^2+4)/(2(a-2)(a+2))-2/(a(a+2))] =
= (a-2)/(4(a+2)^2) : [a*a*(a+2)-(a^2+4)*a-2*2(a-2)] / [2a(a-2)(a+2)] =
= (a-2)/(4(a+2)^2) : (a^3+2a^2-a^3-4a-4a+8)/(2a(a^2-4)) =
= (a-2)/(4(a+2)^2) : (2a^2-8a+8)/(2a(a^-4)) =
= (a-2)/(4(a+2)^2 : (2(a-2)^2/(2a(a-2)(a+2)) =
= (a-2)/(4(a+2)^2 * (a(a+2))/(a-2) = a/(4(a+2))