ГДЗ Алгебра 8 клас Бевз (2025)

86. Спрости вираз.

а) (〖6a〗^2+15ab-8ac-20bc)/(〖12a〗^2-9ab-16ac+12bc) = (3a(2a+5b)-4c(2a+5b))/(3a(4a-3b)-4c(4a-3b)) = ((2a+5b)(3a-4c))/((4a-3b)(3a-4c)) = (2a+5b)/(4a-3b).
б) (〖2a〗^2-18)/(a^2+2a-15) = (2(a-3)(a+3))/(a^2+2a+1-16) = (2(a-3)(a+3))/(〖(a+1)〗^2-16) = (2(a-3)(a+3))/((a+1+4)(a+1-4)) = (2(a-3)(a+3))/((a+5)(a-3)) = (2(a+3))/(a+5);
в) (〖x(y+1)〗^2- 〖y(x+1)〗^2)/(x(y+1)- y(x+1)) = (〖xy〗^2+2xy+ x-〖yx〗^2-2xy- y)/(xy+ x- yx- y) = (-xy(x- y)+(x- y))/(x- y) = ((x-y)(1- xy))/(x- y) = 1 – xy.