Вправи 1001 - 1100 » 1098

1098. Спрости вираз. a) (a+4)/(a-3) – (〖4a〗^2- 1)/(〖2a〗^2- 3a+1) • (a^2+ 2a-3)/(a^2- 9) = (a+4)/(a-3) – ((2a-1)(2a+1))/((2a-1)(a-1)) • ((a+3)(a-1))/((a-3)(a+3)) = (a+4)/(a-3) – (2a+1)/(a-3) = (a+4-2a-1)/(a-3) = (3-a)/(a-3) = –(a-3)/(a-3) = –1. б) ((2a-5)/(a+2) – a/(a-3) + 15/(a^2- a-6)) : (a-10)/(a^2+ 2a) = (〖2a-5〗^(\a-3)/(a+2) – a^(\a+2)/(a-3) + 15/((a-3)(a+2))) • (a(a+2))/(a-10) = (〖2a〗^2-6a-5a+15-a^2-2a+15)/((a+2)(a-3)) • (a(a+2))/(a-10) = (a^2- 13a+30)/(a-3) • a/(a-10) = ((a-10)(a-3))/(a-3) • a/(a-10) = a. в) (x/(x^2+ 6x+8) – 2/(x^2+ 3x+2) + 6/(x^2+ 5x+4)) • (x^2+ 2x)/(x-3) – 3/(x-3) = (x^(\x+1)/((x+4)(x+2)) – 2^(\x+4)/((x+1)(x+2)) + 6^(\x+2)/((x+4)(x+1)) • (x(x+2))/(x-3) – 3/(x-3) = (x^2+ x-2x-8+6x+12)/((x+1)(x+2)(x+4)) • (x(x+2))/(x-3) – 3/(x-3) = (x^2+ 5x+4)/((x+1)(x+4)) • x/(x-3) – 3/(x-3) = ((x+4)(x+1))/((x+1)(x+4)) • x/(x-3) – 3/(x-3) = x/(x-3) – 3/(x-3) = (x-3)/(x-3) = 1.