Question

Сократить дробь (x²-y²-2yz-z²)/(x²+xz-y²-yz)

Answer 1

Применяем формулы сокращенного умножения, группируем, сокращаем:

[x^2-y^2-2yz-z^2]/[x^2+xz-y^2-yz] = [x^2-(y^2+2yz-z^2)]/[(x^2-y^2)+xz-yz]=

[x^2-(y+z)^2]/[(x-y)(x+y)+z(x-y)]=[(x-y-z)(x+y+z)/[(x-y)(x+y+z)] = (x-y-z)/(x-y)

Удачи вам!

Answer 2

$\frac{x^2-y^2-2yz-z^2}{x^2+xz-y^2-yz}=\frac{x^2-(y^2+2yz+z^2)}{(x^2-y^2)+(xz-yz)}=\frac{x^2-(y+z)^2}{(x-y)(x+y)+z(x-y)}=\\\\=\frac{(x-y-z)(x+y+z)}{(x-y)(x+y+z)}= \frac{x-y-z}{x-y}$