ГДЗ Алгебра 8 клас Мерзляк (2025)

Спростіть вираз:

1) (m+n)/(m-n) – (m^2+ n^2)/(m^2- n^2 ) = (m+ n^(\m+n))/(m-n) – (m^2+ n^2)/((m-n)(m+n)) = ((m+n)^2- (m^2+ n^2))/((m-n)(m+n)) = (m^2+ 2mn+ n^2- m^2- n^2)/( (m-n)(m+n)) = 2mn/(m^2- n^2 );
2) (x-y)/(x+y) + y^2/(2xy+ x^2+ y^2 ) = (x- y^(\x+y))/(x+y) + y^(2\1)/((x+y)^2 ) = ((x+y)(x-y)+ y^2)/((x+y)^2 ) = (x^2- y^2+ y^2)/((x+y)^2 ) = x^2/((x+y)^2 );
3) 2a/(4a^2- 1) – (a+4)/(2a^2+ a) = (2a^(\a))/((2a-1)(2a+1)) – (a+ 4^(\2a-1))/(a(2a+1)) = (2a^2- (2a-1)(a+4))/(a(2a-1)(2a+1)) = (2a^2- (2a^2+ 8a-a-4))/(a(2a-1)(2a+1)) = (2a^2- 2a^2- 7a+4)/(a(2a-1)(2a+1)) = (4-7a)/(4a^3- a);