Сократите дробь:
а) $\frac{x^2 - y^2}{3x - 2x^2 + 3y - 2xy}$;
б) $\frac{x^2 - yz + xz - y^2}{x^2 + yz - xz - y^2}$;
в) $\frac{a^2 - c^2}{a^2 + ac - ax - cx}$;
г) $\frac{12z^2 - 9rz + 4nz - 3rn}{20z^2 + 3rn - 15rz - 4nz}$.
$\frac{x^2 - y^2}{3x - 2x^2 + 3y - 2xy} = \frac{(x - y)(x + y)}{(3x + 3y) - (2x^2 + 2xy)} = \frac{(x - y)(x + y)}{3(x + y) - 2x(x + y)} = \frac{(x - y)(x + y)}{(x + y)(3 - 2x)} = \frac{x - y}{3 - 2x}$
$\frac{x^2 - yz + xz - y^2}{x^2 + yz - xz - y^2} = \frac{(x^2 - y^2) + (xz - yz)}{(x^2 - y^2) - (xz - yz)} = \frac{(x - y)(x + y) + z(x - y)}{(x - y)(x + y) - z(x - y)} = \frac{(x - y)(x + y + z)}{(x - y)(x + y - z)} = \frac{x + y + z}{x + y - z}$
$\frac{a^2 - c^2}{a^2 + ac - ax - cx} = \frac{(a - c)(a + c)}{(a^2 + ac) - (ax + cx)} = \frac{(a - c)(a + c)}{a(a + c) - x(a + c)} = \frac{(a - c)(a + c)}{(a + c)(a - x)} = \frac{a - c}{a - x}$
$\frac{12z^2 - 9rz + 4nz - 3rn}{20z^2 + 3rn - 15rz - 4nz} = \frac{(12z^2 - 9rz) + (4nz - 3rn)}{(20z^2 - 15rz) - (4nz - 3rn)} = \frac{3z(4z - 3r) + n(4z - 3r)}{5z(4z - 3r) - n(4z - 3r)} = \frac{(4z - 3r)(3z + n)}{(4z - 3r)(5z - n)} = \frac{3z + n}{5z - n}$
Пожауйста, оцените решение
