Вправи 101 - 200 » 165 (1-5)

165. Спростіть вираз: 1) (a^(\4)/3 + a^(\3)/4) • 6/a^2 = (4a+3a)/12 • 6/a^2 = (7a • 6)/(12a^2 ) = 7/2a; 2) (a^2 b)/(a-b) • (1^(\a)/b – 1^(\b)/a) = (a^2 b • (a-b))/(a-b)ba = a/1 = a; 3) (1\b + a/b) : (1\b – a/b) = (b+a)/b : (b-a)/b = (a+b)b/(b(b-a)) = (a+b)/(b-a); 4) (a^2/b^2 – (2a^(\b))/b + 1^(\b^2 )) • b/(a-b) = (a^2- 2ab+ b^2)/b^2 • b/(a-b) = ((a-b)^2 • b)/(b^2 • (a-b)) = (a-b)/b; 5) (a^2- ab)/(b^2- 1) • (b+1)/a – a/(b-1) = (a(a-b)•(b+1))/(b-1)(b+1)a = (a-b)/(b-1) – a/(b-1) = (a-b-a)/(b-1) = –b/(1-b);