Вправи 101 - 200 » 167 (1-3)

167. Виконайте дії: 1) (a+2)/(a^2- 2a+1) : (a^2- 4)/(3a-3) – 3/(a-2) = ((a+2) • 3 • (a-1))/((a-1)^2 (a-2)(a+2)) – 3/(a-2) = 3/((a-1)(a-2)) – 3^(\a-1)/(a-2) = (3-3(a-1))/((a-1)(a-2)) = (3-3a+3)/((a-1)(a-2)) = (6-3a)/((a-1)(a-2)) = (-3(a-2))/((a-1)(a-2)) = –3/(a-1) = 3/(1-a); 2) (b^2+ 3b)/(b^3+ 9b) • ((b-3)/(b+3) + (b+3)/(b-3)) = (b(b+3))/(b(b^2+ 9)) • ((b-3)^2+ (b+3)^2)/((b-3)(b+3)) = ((b+3)•(b^2- 6b+9+ b^2+ 6b+9))/(b(b^2+ 9)(b-3)(b+3)) = ((b+3)(2b^2+ 18))/(b(b^2+ 9)(b-3)(b+3)) = (2(b^2+ 9))/((b^2+ 9)(b-3)) = 2/(b-3); 3) ((3c+ 1^(\3c+1))/(3c -1) – (3c- 1^(\3c-1))/(3c+1)) : 2c/(6c+2) = ((3c+1)^1- (3c-1)^2)/((3c-1)(3c+1)) • (2(3c+1))/2c = (9c^2+ 6c+1-(9c^2- 6c+1))/((3c-1)(3c+1)) • (3c+1)/c = (9c^2+ 6c+1-9c^2+ 6c-1)/((3c-1)(3c+1)) • (3c+1)/c = (12c(3c+1))/((3c-1)(3c+1) • c) = 12/(3c-1);