Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ » 7.11

Спростіть вираз: 1) 16/(x+2) : ((x+2)/(x-2) – 16/(x^2- 4) – (x-2)/(x+2)) = 2. 1. (x+2)/(x-2) – 16/(x^2- 4) – (x-2)/(x+2) = ((x+2)^2-16-(x-2)^2)/((x-2)(x+2)) = (x^2+ 4x+4-16-x^2 +4x-4)/((x-2)(x+2)) = (8x-16)/((x-2)(x+2)) = (8(x-2))/((x-2)(x+2)) = 8/(x+2); 2. 16/(x+2) : 8/(x+2) = (16(x+2))/((x+2) • 8) = 2. 2) ((5a+1)/(a-2) + (5a-1)/(a+2)) • (a^2- 4)/(5a^2+2) = 2. 1. (5a+1)/(a-2) + (5a-1)/(a+2) = ((5a+1)(a+2)+(5a-1)(a-2))/((a-2)(a+2)) = (5a^2+10a+ a+2+5a^2-10a- a+2)/((a-2)(a+2)) = (10a^2+4)/(a^2- 4); 2. (10a^2+4)/(a^2- 4) • (a^2- 4)/(5a^2+2) = (2(5a^2+2)(a^2 -4))/((a^2 -4)(5a^2+2)) = 2.