РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 155

155. Спростіть вираз: 1) 2^(\x-3)/(3+x) – 2x/(x^2- 9) = (2x-6-2x)/(x^2- 9) = –6/(x^2- 9); 2) 4x/(x^2- 25) – 4/(x-5) = 4x/((x-5)(x+5)) – 4^(\x+5)/(x-5) = (4x-4x-20)/((x-5)(x+5)) = –20/(x^2- 25); 3) 2/(6+c) + 2c/〖36-c〗^2 = 2^(\6-c)/(6+c) + 2c/((6-c)(6+c)) = (12-2c+2c)/((6-c)(6+c)) = 12/〖36-c〗^2 ; 4) 5/(x+7) – 10x/(x^2- 49) = 5^(\x-7)/(x+7) – 10x/((x-7)(x+7)) = (5x-35-10x)/((x-7)(x+7)) = –(-5x-35)/(x^2- 49); 5) 2/(y+1) – (1+2y)/(y^2- 1) = 2^(\y-1)/(y+1) – (1+2y)/((y-1)(y+1)) = (2y-2-1-2y)/((y-1)(y+1)) = –3/((y-1)(y+1)); 6) 4/(c^2- 4) – (4-c)/(c-2) = 4/((c-2)(c+2)) – 〖4-c〗^(\c+2)/(c-2) = (〖4-(4c+8-c〗^2- 2c))/((c-2)(c+2)) = (4-4c-8+ c^2+ 2c)/(c^2- 4) = (c^2- 2c-4)/(c^2- 4).