$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{xy} = \frac{xy(12xy^2z - 3yz^2 + 4yz^3)}{xy} = 12xy^2z - 3yz^2 + 4yz^3$.
Ответ: xy

$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{xy^2z} = \frac{xy^2z(12xy - 3z + 4z^2)}{xy^2z} = 12xy - 3z + 4z^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{5z} = \frac{5z(2,4x^2y^3 - 0,6xy^2z + 0,8xy^2z^2)}{5z} = 2,4x^2y^3 - 0,6xy^2z + 0,8xy^2z^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{6xyz} = \frac{6xyz(2xy^2 - \frac{1}{2}yz + \frac{2}{3}yz^2)}{6xyz} = 2xy^2 - \frac{1}{2}yz + \frac{2}{3}yz^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{20xy} = \frac{20xy(0,6xy^2z - 0,15yz^2 + 0,2yz^3)}{20xy} = 0,6xy^2z - 0,15yz^2 + 0,2yz^3$.
Ответ: $xy^2z; 5z; 6xyz; 20xy$.

$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{y^2} = \frac{y^2(12x^2yz - 3xz^2 + 4xz^3)}{y^2} = 12x^2yz - 3xz^2 + 4xz^3$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{3} = \frac{3(4x^2y^3z - xy^2z^2 + \frac{4}{3}xy^2z^3)}{3} = 4x^2y^3z - xy^2z^2 + 1\frac{1}{3}xy^2z^3$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{142xyz} = \frac{142xyz(\frac{12}{142}xy^2 - \frac{3}{142}yz + \frac{4}{142}yz^2)}{142xyz} = \frac{6}{71}xy^2 - \frac{3}{142}yz + \frac{2}{71}yz^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{15x} = \frac{15x(\frac{12}{15}xy^3z - \frac{3}{15}y^2z^2 + \frac{4}{15}y^2z^3)}{15x} = \frac{4}{5}xy^3z - \frac{1}{5}y^2z^2 + \frac{4}{15}y^2z^3$.
Ответ: $y^2; 3; 142xyz; 15x$.

$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{4xy^2} = \frac{4xy^2(3xyz - 0,75z^2 + z^3)}{4xy^2} = 3xyz - 0,75z^2 + z^3$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{y^2z} = \frac{y^2z(12x^2y - 3xz + 4xz^2)}{y^2z} = 12x^2y - 3xz + 4xz^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{8} = \frac{8(1,5x^2y^3z - 0,375xy^2z^2 + 0,5xy^2z^3)}{8} = 1,5x^2y^3z - 0,375xy^2z^2 + 0,5xy^2z^3$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{7xyz} = \frac{7xyz(\frac{12}{7}xy^2 - \frac{3}{7}yz + \frac{4}{7}yz^2)}{7xyz} = 1\frac{5}{7}xy^2 - \frac{3}{7}yz + \frac{4}{7}yz^2$;
$\frac{12x^2y^3z - 3xy^2z^2 + 4xy^2z^3}{2xy^2z} = \frac{2xy^2z(6xy - 1,5z + 2z^2)}{2xy^2z} = 2xy^2z(6xy - 1,5z + 2z^2$.
Ответ: $4xy^2; y^2z; 8; 7xyz; 2xy^2z$.