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ГДЗ Алгебра 8 клас Мерзляк (2025)
§ 1. Раціональні вирази
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4) (b-2)/(b^2+ 6b+9) – b/(b^2- 9) = (b- 2^(\b-3))/((b+3)^2 ) – b^(\b+3)/((b-3)(b+3)) = ((b-2)(b-3)- b(b+3))/((b+3)^2 (b-3)) = (b^2- 3b-2b+6- b^2- 3b)/((b+3)^2 (b-3)) = (6-8b)/((b+3)^2 (b-3));
5) (x-6)/(x^2+ 3x) + x/(x+3) – (x-3)/x = (x-6)/(x^2+ 3x) + x^(\x)/(x+3) – (x- 3^(\x+3))/x = (x-6+ x^2- (x^2- 9))/(x(x+3)) = (x-6+ x^2- x^2+ 9)/(x(x+3)) = (x+3)/(x(x+3)) = 1/x;
6) (y+2)/(y-2) – (y-2)/(y+2) – 16/(y^2- 4) = (y+ 2^(\y+2))/(y-2) – (y- 2^(\y-2))/(y+2) – 16/(y^2- 4) = ((y+2)^2- (y-2)^2- 16)/((y-2)(y+2)) = (y^2+ 4y+4-(y^2- 4y+4)- 16)/((y-2)(y+2)) = (y^2+ 4y+4- y^2+ 4y-4-16)/((y-2)(y+2)) = (8y-16)/((y-2)(y+2)) = (8(y-2))/((y-2)(y+2)) = 8/(y+2).
5) (x-6)/(x^2+ 3x) + x/(x+3) – (x-3)/x = (x-6)/(x^2+ 3x) + x^(\x)/(x+3) – (x- 3^(\x+3))/x = (x-6+ x^2- (x^2- 9))/(x(x+3)) = (x-6+ x^2- x^2+ 9)/(x(x+3)) = (x+3)/(x(x+3)) = 1/x;
6) (y+2)/(y-2) – (y-2)/(y+2) – 16/(y^2- 4) = (y+ 2^(\y+2))/(y-2) – (y- 2^(\y-2))/(y+2) – 16/(y^2- 4) = ((y+2)^2- (y-2)^2- 16)/((y-2)(y+2)) = (y^2+ 4y+4-(y^2- 4y+4)- 16)/((y-2)(y+2)) = (y^2+ 4y+4- y^2+ 4y-4-16)/((y-2)(y+2)) = (8y-16)/((y-2)(y+2)) = (8(y-2))/((y-2)(y+2)) = 8/(y+2).