Вправи для повторення розділу 3 » 38 (2)

2) (2x^2- 7)/(x^2- 3x-4) – (x+1)/(x-4). x2 – 3x – 4 = 0; D = (–3)2 – 4 • (–4) = 25; x1 = (3+5)/2 = 4; x2 = (3-5)/2 = –1. (2x^2- 7)/((x-4)(x+1)) – (x+1)/(x-4) = (2x^2- 7-(x+1)^2)/((x-4)(x+1)) = (2x^2- 7- x^2- 2x-1)/((x-4)(x+1)) = (x^2- 2x-8)/((x-4)(x+1)). x2 – 2x – 8 = 0; D = (–2)2 – 4 • (–8) = 36; x1 = (2+6)/2 = 4; x2 = (2-6)/2 = –2. (x^2- 2x-8)/((x-4)(x+1)) = ((x-4)(x+2))/((x-4)(x+1)) = (x+2)/(x+1).