Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.34

Спростіть вираз: 1) ((x-1)/(2x^2+ 3x+1) – 1/(x^2- 1)) : (x-4)/(x^3- x) = x^2/(2x+1). 1. 2x2 + 3x + 1 = 0; D = 32 – 4 • 1 • 1 = 1; x1 = (-3+1)/4 = –1/2; x2 = (-3-1)/4 = –1. 2. (x-1)/(2(x+1)(x+ 1/2)) – 1/((x-1)(x+1)) = ((x-1)^2- (2x+1))/((x+1)(2x+1)(x-1)) = (x^2- 2x+1-2x-1)/((x+1)(2x+1)(x-1)) = (x^2- 4x)/((x+1)(2x+1)(x-1)). 3. (x^2- 4x)/((x+1)(2x+1)(x-1)) : (x-4)/(x^3- x) = (x(x-4)x(x^2- 1))/((x^2- 1)(2x+1)(x-4)) = x^2/(2x+1). 2) (3b – 9)2 • (b/(b^2- 6b+ 9) – (b+2)/(b^2- b-6)) = 27. 1. b2 – b – 6 = 0; D = 12 – 4 • (–6) = 25; b1 = (1+5)/2 = 3; b2 = (1-5)/2 = –2. 2. b/((b-3)^2 ) – (b+2)/((b+2)(b-3)) = b/((b-3)^2 ) – 1/(b-3) = (b-(b-3))/((b-3)^2 ) = 3/((b-3)^2 ). 3. (3(b – 3))2 • 3/((b-3)^2 ) = (9(b-3)^2 • 3)/((b-3)^2 ) = 27.