Сократите дробь:
а) $\frac{3x^2 - 6xy + 3y^2}{6x^2 - 6y^2}$;
б) $\frac{m^2 + 6mn + 9n^2}{4m^2 + 12mn}$;
в) $\frac{40c^2 - 10d^2}{20c^2 + 20cd + 5d^2}$;
г) $\frac{4n^2 - 4n + 1}{2n - 4n^2}$.
$\frac{3x^2 - 6xy + 3y^2}{6x^2 - 6y^2} = \frac{3(x^2 - 2xy + y^2)}{6(x^2 - y^2)} = \frac{(x - y)^2}{2(x - y)(x + y)} = \frac{x - y}{2(x + y)}$
$\frac{m^2 + 6mn + 9n^2}{4m^2 + 12mn} = \frac{(m + 3n)^2}{4m(m + 3n)} = \frac{m + 3n}{4m}$
$\frac{40c^2 - 10d^2}{20c^2 + 20cd + 5d^2} = \frac{10(4c^2 - d^2)}{5(4c^2 + 4cd + d^2)} = \frac{2(2c - d)(2c + d)}{(2c + d)^2} = \frac{2(2c - d)}{2c + d}$
$\frac{4n^2 - 4n + 1}{2n - 4n^2} = \frac{(2n - 1)^2}{2n(1 - 2n)} = \frac{(1 - 2n)^2}{2n(1 - 2n)} = \frac{1 - 2n}{2n}$
Пожауйста, оцените решение
