ГДЗ зошит Алгебра 8 клас Тарасенкова

6. Спростіть вираз.

1) (xy/(x^2- y^2 ) + y/(2y-2x)) : 2y/(x^2-y^2 ) = (〖xy〗^(\2)/((x- y)(x+ y)) + y^(\x+y)/(2(y- x))) • ((x- y)(x+ y))/2y = (〖(2xy- xy- y〗^2)•(x- y)(x+ y))/(2(x- y)(x+y)•2y) = 〖xy- y〗^2/4y = (y(x- y))/4y = (x- y)/4;
2) (x^2+5x+4)/(x^2+2x-8) • ((x^2-1)/(x^2-4))–1;
x² + 5x + 4 = 0;
x1x2 = 4; x1 + x2 = –5; x1 = –1, x2 = –4.
x² + 2x – 8 = 0; x1x2 = –8; x1 + x2 = –2;
x1 = 2; x2 = –4.
((x+1)(x+4)(x-2)(x+2))/((x-2)(x+4)(x-1)(x+1)) = (x+2)/(x-1).