Вправи 101 - 200 » 169 (1-2)

169. Спростіть вираз: 1) (15/(x-7) – x – 7) • (7-x)/(x^2- 16x+64) = (x+8)/(x-8). 1. 15/(x-7) – (x + 7) = 15/(x-7) – (x+ 7^(\x-7))/1 = (15-(x-7)(x+7))/(x-7) = (15-(x^2- 49))/(x-7) = (15- x^2+ 49)/(x-7) = (64- x^2)/(x-7); 2. ((8-x)(8+x))/( x-7) • (7-x)/((x-8)^2 ) = (-(x-8)(x+7)•(-(x-7)))/((x-7)(x-8)^2 ) = (x+8)/(x-8); 2) (a – (5a-16)/(a-3)) : (2a – 2a/(a-3)) = (a-4)/2a. 1. a^(\a-3)/1 – (5a-16)/(a-3) = (a(a-3)- (5a-16))/(a-3) = (a^2- 3a-5a+16)/(a-3) = (a^2- 8a+16)/(a-3) = ((a-4)^2)/(a-3); 2. 〖2a〗^(a-3)/1 – 2a/(a-3) = (2a(a-3)- 2a)/(a-3) = (2a^2- 6a-2a)/(a-3) = (2a^2- 8a)/(a-3) = (2a(a-4))/(a-3); 3. ((a-4)^2)/(a-3) : (2a(a-4))/(a-3) = ((a-4)^2•(a-3))/((a-3)•2a(a-4)) = (a-4)/2a;