Выполните сокращение:
а) $\frac{b^{14} - b^7 + 1}{b^{21} + 1}$;
б) $\frac{x^{33} - 1}{x^{33} + x^{22} + x^{11}}$;
в) $\frac{x(y - x) - y(x - z)}{x(y - x)^2 - y(x - z)^2}$;
г) $\frac{a(b + 1)^2 - b(a + 1)^2}{a(b + 1) - b(a + 1)}$.
$\frac{b^{14} - b^7 + 1}{b^{21} + 1} = \frac{b^{14} - b^7 + 1}{(b^7 + 1)(b^{14} - b^7 + 1)} = \frac{1}{b^7 + 1}$
$\frac{x^{33} - 1}{x^{33} + x^{22} + x^{11}} = \frac{(x^{11} - 1)(x^{22} + x^{11} + 1)}{x^{11}(x^{22} + x^{11} + 1)} = \frac{x^{11} - 1}{x^{11}}$
$\frac{x(y - x) - y(x - z)}{x(y - x)^2 - y(x - z)^2} = \frac{xy - xz - xy + yz}{x(y^2 - 2yz + x^) - y(x^2 - 2xz + z^2)} = \frac{z(y - x)}{xy^2 - 2xyz + xz^2 - x^2y + 2xyz - yz^2} = \frac{z(y - x)}{xy(y - x) - z^2(y - x)} = \frac{z(y - x)}{(xy - z^2)(y - x)} = \frac{z}{xy - z^2}$
$\frac{a(b + 1)^2 - b(a + 1)^2}{a(b + 1) - b(a + 1)} = \frac{a(b^2 + 2b + 1) - b(a^2 + 2a + 1)}{ab + a - ab - b} = \frac{ab^2 + 2ab + a - a^2b - 2ab - b}{a - b} = \frac{ab(b - a) + a - b}{a - b} = \frac{(a - b)(1 - ab)}{a - b} = 1 - ab$
Пожауйста, оцените решение
