ГДЗ зошит Алгебра 8 клас Тарасенкова

6. Спростіть вираз.

1) (y/(x^2- xy) + y/(y^2-xy)) : (x+ y)/xy = (y/(x(x- y)) + x/(y(y- x))) • xy/(x+ y) = (y^(\y)/(x(x-y)) – x^2/(y(x- y))) • xy/(x+ y) = ((y^2- x^2)xy)/(xy(x- y)(x+ y)) = ((y- x)(y+ x))/((x- y)(x+ y)) = –1
2) (x^2+8x+15)/(x^2-3x-18) • ((x^2-25)/(x^2-36))–1 =
x² + 8x + 15 = 0; x1x2 = 15; x1 + x2 = –8;
x1 = –3; x2 = –5.
x² – 3x – 18 = 0; x1x2 = –18;
x1 + x2 = 3; x1 = 6; x2 = –3.
= ((x+3)(x+5)(x-6)(x+6))/((x+3)(x-6)(x-5)(x+5)) = (x+6)/(x-5).