Сократите дробь:
а) $\frac{18x^5 - 72x^3y^2}{12x^3y^2 - 48x^2y^3 + 48xy^4}$;
б) $\frac{72a^2bc^3 - 96a^4bc^2 + 32a^6bc}{16a^5b^2c^3 - 36ab^2c^5}$;
в) $\frac{135a^3b^3 + 180a^2b^4 + 60ab^5}{225a^5b - 100a^3b^3}$;
г) $\frac{150x^5y^2z - 24x^3y^6z}{40xy^5z^2 - 200x^2y^3z^2 + 250x^3yz^2}$.
$\frac{18x^5 - 72x^3y^2}{12x^3y^2 - 48x^2y^3 + 48xy^4} = \frac{18x^3(x^2 - 4y^2)}{12xy^2(x^2 - 4xy + 4y^2)} = \frac{3x^2(x - 2y)(x + 2y)}{2y^2(x - 2y)^2} = \frac{3x^2(x + 2y)}{2y^2(x - 2y)}$
$\frac{72a^2bc^3 - 96a^4bc^2 + 32a^6bc}{16a^5b^2c^3 - 36ab^2c^5} = \frac{8a^2bc(9c^2 - 12a^2c + 4a^4)}{4ab^2c^3(4a^4 - 9c^2)} = \frac{2a(3c - 2a^2)^2}{bc^2(2a^2 - 3c)(2a^2 + 3c)} = \frac{2a(2a^2 - 3c)^2}{bc^2(2a^2 - 3c)(2a^2 + 3c)} = \frac{2a(2a^2 - 3c)}{bc^2(2a^2 + 3c)}$
$\frac{135a^3b^3 + 180a^2b^4 + 60ab^5}{225a^5b - 100a^3b^3} = \frac{15ab^3(9a^2 + 12ab + 4b^2)}{25a^3b(9a^2 - 4b^2)} = \frac{3b^2(3a + 2b)^2}{5a^2(3a - 2b)(3a + 2b)} = \frac{3b^2(3a + 2b)}{5a^2(3a - 2b)}$
$\frac{150x^5y^2z - 24x^3y^6z}{40xy^5z^2 - 200x^2y^3z^2 + 250x^3yz^2} = \frac{6x^3y^2z(25x^2 - 4y^4)}{10xyz^2(4y^4 - 20xy^2 + 25x^2)} = \frac{3x^2y(5x - 2y^2)(5x + 2y^2)}{5z(2y^2 - 5x)^2} = \frac{3x^2y(5x - 2y^2)(5x + 2y^2)}{5z(5x - 2y^2)^2} = \frac{3x^2y(5x + 2y^2)}{5z(5x - 2y^2)}$
Пожауйста, оцените решение
