Вправи 201 - 300 » 208

207. Спростіть вираз: 1) (〖x+5〗^(\x+1)/(5x-1) + 〖x+5〗^(\5x-1)/(x+1)) • (1-5x)/(x^2+ 5x) + (x^2+ 5)/(x+1) = (x^2+ x+5x+5+ 〖5x〗^2- x+25x-5)/((5x-1)(x+1)) • (–(5x-1)/(x^2+ 5x)) + (x^2+ 5)/(x+1) = (〖6x〗^2+ 30x)/((5x-1)(x+1)) • (–(5x-1)/(x^2+ 5x)) + (x^2+ 5)/(x+1) = (6x(x+5))/((5x-1)(x+1)) • (–(5x-1)/(x(x+5))) + (x^2+ 5)/(x+1) = (6x(x+5)(5x-1))/((5x-1)(x+1)•x(x+5)) + (x^2+ 5)/(x+1) = –6/(x+1) + (x^2+ 5)/(x+1) = (-6+ x^2+ 5)/(x+1) = ((x-1)(x+1))/(x+1) = x – 1. 2) (〖a-3〗^(\a-4)/(7a-4) – 〖a-3〗^(\7a-4)/(a-4)) • (7a-4)/〖9a-3a〗^2 + (a^2- 14)/(4-a) = (a^2- 4a-3a+12-(〖7a〗^2- 4a-21a+12))/((7a-4)(a-4)) • (7a-4)/(3a(3-a)) + (a^2- 14)/(4-a) = (a^2- 7a+12- 〖7a〗^2+ 25a-12)/((7a-4)(a-4)) • (7a-4)/(3a(3-a)) + (a^2- 14)/(4-a) = (〖-6a〗^2+ 18a)/((7a-4)(a-4)) • (7a-4)/( 3a(3-a)) + (a^2- 14)/(4-a) = (-6a(a-3))/((7a-4)(a-4)) • (7a-4)/(3a(3-a)) + (a^2- 14)/(4-a) = –(6a(a-3)•(7a-4))/((7a-4)(a-4)•3a(3-a)) + (a^2- 14)/(4-a) = (2(a-3))/((a-4)(a-3)) + (a^2- 14)/(4-a) = 2/(a-4) – (2- a^2+ 14)/(a-4) = 〖16-a〗^2/(a-4) = ((4-a)(4+a))/(a-4) = –a – 4.