ГДЗ Алгебра 8 клас Тарасенкова (2025)

Скоротіть дріб:

1) (a^2-b^2- c^2-2bc )/(a^2+ b^2- c^2-2ab) = (a^2- 〖(b+ c)〗^2)/(〖(a+ b)〗^2- c^2 ) = ((a-(b+ c))(a+ b+ c))/((a+ b- c)(a+ b+ c)) = (a-b - c)/(a+ b- c);
2) ((a- b)(c- d))/(〖(b〗^2- a^2)(d^2-c^2) ) = ((a- b)(c- d))/((b- a)(b+ a)(d- c)(d+ c)) = ((a- b)(c- d))/((a- b)(a+ b)(c- d)(c+ d)) = 1/((a+ b)(c+ d));
3) (x^2+ xy+ yz-z^2 )/(y^2- x^2+2xz-z^2 ) = (x^2-z^2+ y(x+ z) )/(y^2- 〖(x- z)〗^2 ) = ((x- z)(x+ z)+ y(x+ z))/((y-(x- z))(y+(x- z)) = ((x+ z)(x- z+ y))/((y- x+ z)(x- z + y)) = (x+ z)/(y- x+ z);
4) (〖25- a〗^2-〖2ab- b〗^2 )/(a^2+ ab+5b-25) = 〖25-(a+ b)〗^2/(〖(a〗^2-25)+(ab+5b)) = ((5-(a+ b))(5+(a+ b))/((a-5)(a+5)+ b(a+5)) = ((5- a- b)(5+ a+ b))/((a+5)(a-5+ b)) = –((a+ b-5)(a+ b+5))/((a+5)(a+ b-5)) = –(a+ b+5)/(a+5).