Сократите дробь:
а) $\frac{a^3 - a^2 - a + 1}{a^4 - 2a^2 + 1}$;
б) $\frac{x^2 + y^2 - z^2 + 2xy}{x^2 - y^2 + z^2 + 2xz}$.
$\frac{a^3 - a^2 - a + 1}{a^4 - 2a^2 + 1} = \frac{(a^3 - a^2) - (a - 1)}{(a^2 - 1)^2} = \frac{a^2(a - 1) - (a - 1)}{(a^2 - 1)^2} = \frac{(a - 1)(a^2 - 1)}{(a^2 - 1)^2} = \frac{a - 1}{a^2 - 1} = \frac{a - 1}{(a - 1)(a + 1)} = \frac{1}{a + 1}$
$\frac{x^2 + y^2 - z^2 + 2xy}{x^2 - y^2 + z^2 + 2xz} = \frac{(x^2 + 2xy + y^2) - z^2}{(x^2 + 2xz + z^2) - y^2} = \frac{(x + y)^2 - z^2}{(x + z)^2 - y^2} = \frac{(x + y - z)(x + y + z)}{(x + z - y)(x + z + y)} = \frac{x + y - z}{x + z - y}$
Пожаулйста, оцените решение
