Сократите дробь:
а) $\frac{2m - 2n + 3mn - 3n^2}{16m + 54mn^3}$;
б) $\frac{8x^2 + 10xy}{4x^2 + 5xy - 4x - 5y}$;
в) $\frac{a - b + 4ab - 4b^2}{48ab^3 + 3ab + 24ab^2}$;
г) $\frac{p^3 + p^2}{3p^2 + 4pq + 3p + 4q}$.
$\frac{2m - 2n + 3mn - 3n^2}{16m + 54mn^3} = \frac{(2m - 2n) + (3mn - 3n^2)}{2m(8 + 27n^3)} = \frac{2(m - n) + 3n(m - n)}{2m(2 + 3n)(4 - 6n + 9n^2)} = \frac{(m - n)(2 + 3n)}{2m(2 + 3n)(4 - 6n + 9n^2)} = \frac{m - n}{2m(4 - 6n + 9n^2)}$
$\frac{8x^2 + 10xy}{4x^2 + 5xy - 4x - 5y} = \frac{2x(4x + 5y)}{(4x^2 + 5xy) - (4x + 5y)} = \frac{2x(4x + 5y)}{x(4x + 5y) - (4x + 5y)} = \frac{2x(4x + 5y)}{(4x + 5y)(x - 1)} = \frac{2x}{x - 1}$
$\frac{a - b + 4ab - 4b^2}{48ab^3 + 3ab + 24ab^2} = \frac{(a - b) + (4ab - 4b^2)}{3ab(16b^2 + 1 + 8b} = \frac{(a - b) + 4b(a - b)}{3ab(16b^2 + 8b + 1} = \frac{(a - b)(1 + 4b)}{3ab(4b + 1)^2} = \frac{a - b}{3ab(4b + 1)}$
$\frac{p^3 + p^2}{3p^2 + 4pq + 3p + 4q} = \frac{p^2(p + 1)}{(3p^2 + 3p) + (4pq + 4q)} = \frac{p^2(p + 1)}{3p(p + 1) + 4q(p + 1)} = \frac{p^2(p + 1)}{(p + 1)(3p + 4q)} = \frac{p^2}{3p + 4q}$
Пожауйста, оцените решение
