Сократите дробь:
а) $\frac{a^2 - b^2}{a + b}$;
б) $\frac{x - 1}{x^2 - 1}$;
в) $\frac{m^2 - n^2}{2m + 2n}$;
г) $\frac{xm + xn}{m^2 - n^2}$;
д) $\frac{x^2 - 2x + 1}{x^2 - 1}$;
е) $\frac{a^2 - b^2}{b^2 + 2ab + a^2}$;
ж) $\frac{n^2 - m^2}{(n - m)^2}$;
з) $\frac{p - p^2}{p^2 - 1}$;
и) $\frac{x + x^2}{x^3 - x}$;
к) $\frac{a^3 - 2a^2}{4 - a^2}$.
$\frac{a^2 - b^2}{a + b} = \frac{(a - b)(a + b)}{a + b} = a - b$
$\frac{x - 1}{x^2 - 1} = \frac{x - 1}{(x - 1)(x + 1)} = \frac{1}{x + 1}$
$\frac{m^2 - n^2}{2m + 2n} = \frac{(m - n)(m + n)}{2(m + n)} = \frac{m - n}{2}$
$\frac{xm + xn}{m^2 - n^2} = \frac{x(m + n)}{(m - n)(m + n)} = \frac{x}{m - n}$
$\frac{x^2 - 2x + 1}{x^2 - 1} = \frac{(x - 1)^2}{(x - 1)(x + 1)} = \frac{x - 1}{x + 1}$
$\frac{a^2 - b^2}{b^2 + 2ab + a^2} = \frac{(a - b)(a + b)}{(a + b)^2} = \frac{a - b}{a + b}$
$\frac{n^2 - m^2}{(n - m)^2} = \frac{(n - m)(n + m)}{(n - m)^2} = \frac{n + m}{n - m}$
$\frac{p - p^2}{p^2 - 1} = \frac{p(1 - p)}{(p - 1)(p + 1)} = -\frac{p(p - 1)}{(p - 1)(p + 1)} = -\frac{p}{p + 1}$
$\frac{x + x^2}{x^3 - x} = \frac{x(1 + x)}{x(x^2 - 1)} = \frac{x(x + 1)}{x(x - 1)(x + 1)} = \frac{x}{x - 1}$
$\frac{a^3 - 2a^2}{4 - a^2} = \frac{a^2(a - 2)}{(2 - a)(2 + a)} = -\frac{a^2(a - 2)}{(a - 2)(a + 2)} = -\frac{a^2}{a + 2}$
Пожауйста, оцените решение