Вправа 301 - 400 » 306

306. Виконай дії. a) (a^2- 4)/〖9-a〗^2 : (a-2)/(3+a) – 2/(3-a) = ((a-2)(a+2)(3+a))/((3-a)(3+a)(a-2)) – 2/(3-a) = (a+2)/(3-a) – 2/(3-a) = (a+2-2)/(3-a) = a/(3-a); б) (x – 5x/(x+3)) : (x-2)/(x+3) = (x^2+ 3x-5x)/(x+3) • (x+3)/(x-2) = (x^2- 2x)/(x-2) = (x(x-2))/(x-2) = x; в) (a^2- b^2)/(4a+4) • (a+1)/(a-b) + (a+b)/4 = ((a+b)(a+1))/(4(a+1)) + (a+b)/4 = (a+b)/4 + (a+b)/4 = (a+b)/2; г) (2a/(2a-1) + 1) • (6a-3)/(〖4a〗^2- a) = (2a+2a-1)/(2a-1) • (3(2a-1))/(a(4a-1)) = ((4a-1)•3(2a-1))/((2a-1)•a(4a-1)) = 3/a.