Вправа 301 - 400 » 328

328. Спростіть вираз. a) (3/(a-1) – (〖3a〗^2+ 6a+3)/(a^2- 1) : (a^4+ a)/(a^3+ 1)) • 〖a+a〗^2/(-3) = (a+1)/(a-1); 1. 〖3(a+1)〗^2/((a-1)(a+1)) • (a^3+ 1)/(a(a^3+ 1)) = (3(a+1)•1)/((a-1)•a) = (3(a+1))/(a(a-1)); 2. 3/(a-1) – (3a+3)/(a(a-1)) = (3a-3a-3)/(a(a-1)) = (-3)/(a(a-1)) = 3/(a(1-a)); 3. 3/(a(1-a)) • (a(a+1))/(-3) = (a+1)/(a-1); б) (4a/(a+2) – (a^3-8)/(a^3+8) : (a^3-4)/(〖4a〗^2-16a+16))3 • (a+2)/16 = (a^3+8a-8)/(〖2(a〗^3+8)); 1. (a^3-8)/(a^3+8) • (〖4(a〗^2-4a+4))/(a^2-4) = (〖(a〗^3-8)•4• 〖(a-2)〗^2)/(〖(a〗^3+8)(a-2)(a+2)) = (〖4(a〗^3-8)(a-2))/(〖(a〗^3+8)(a+2)); 2. 4a/(a+2) – (〖4(a〗^3-8)(a-2))/(〖(a〗^3+8)(a+2)) = (〖4a(a〗^3+8)- 〖(a〗^3-8)(4a-8))/(〖(a〗^3+8)(a+2)) = (〖4a〗^4+32a-〖4a〗^4+ 〖8a〗^3+32a-64 )/((a^3+8)(a+2)) = (〖8a〗^3+64a-64)/(〖(a〗^3+8)(a+2)); 3. (〖8a〗^3+64a-64)/(〖(a〗^3+8)(a+2)) • (a+2)/16 = (a^3+8a-8)/(〖(a〗^3+8)•2).