977. 1) \(\frac{x^2-2xy}{xy-2y^2}\) ; 2) \(\frac{3x^2+4xy}{9x^2y-16y^3}\) ; 3) \(\frac{2ac-4bc}{5a^3c-20ab^2c}\) ; 4) \(\frac{x^2-2xy}{2y^2-xy}\) ; 5) \(\frac{x^3-2x^2y}{2x^3y^2-x^4y}\)

Решение:

1. \(\frac{x^2-2xy}{xy-2y^2} = \frac{x(x-2y)}{y(x-2y)} = \frac{x}{y}\)

2. \(\frac{3x^2+4xy}{9x^2y-16y^3} = \frac{x(3x+4y)}{y(9x^2-16y^2)} = \frac{x(3x+4y)}{y(3x-4y)(3x+4y)} = \frac{x}{y(3x-4y)}\)

3. \(\frac{2ac-4bc}{5a^3c-20ab^2c} = \frac{2c(a-2b)}{5ac(a^2-4b^2)} = \frac{2(a-2b)}{5a(a-2b)(a+2b)} = \frac{2}{5a(a+2b)}\)

4. \(\frac{x^2-2xy}{2y^2-xy} = \frac{x(x-2y)}{y(2y-x)} = \frac{x(x-2y)}{-y(x-2y)} = -\frac{x}{y}\)

5. \(\frac{x^3-2x^2y}{2x^3y^2-x^4y} = \frac{x^2(x-2y)}{x^3y(2y-x)} = \frac{x^2(x-2y)}{-x^3y(x-2y)} = -\frac{1}{xy}\)

Ответ: 1) \(\frac{x}{y}\); 2) \(\frac{x}{y(3x-4y)}\); 3) \(\frac{2}{5a(a+2b)}\); 4) -\(\frac{x}{y}\); 5) -\(\frac{1}{xy}\).