Вправи 101 - 200 » 170 (1-2)

170. Спростіть вираз: 1) (x^2+ 14x+49)/(x+6) : (13/(x+6) – x + 6) = (7+x)/(7-x). 1. 13/(x+6) – (x – 6) = 13/(x+6) – (x- 6^(\x+6))/1 = (13-(x-6)(x+6))/(x+6) = (13-(x^2- 36))/(x+6) = (13- x^2+ 36)/(x+6) = (49- x^2)/(x+6); 2. ((x+7)^2)/(x+6) • (x+6)/((7-x)(7+x)) = (7+x)/(7-x); 2) (c – (2c-9)/(c+8)) : (c^2+ 3c)/(c^2- 64) + 24/c = c – 5. 1. c^(\c+8)/1 – (2c-9)/(c+8) = (c(c+8)- (2c-9))/(c+8) = (c^2+ 8c-2c+9)/(c+8) = (c^2+ 6c+9)/(c+8); 2. ((c+3)^2)/(c+8) • ((c-8)(c+8))/(c(c+3)) = ((c+3)(c-8))/c = (c^2- 5c-24)/c; 3. (c^2- 5c-24)/c + 24/c = (c^2- 5c-24+24)/c = (c^2- 5c)/c = (c(c-5))/c = c – 5;