Question

Выполнить действия(x-4y)/6x(x-y)-(x+4y)/6x(x+y)

Answer 1

$\frac{x-4y}{6x(x-y)}-\frac{x+4y}{6x(x+y)}=\frac{(x-4y)(x+y)-(x+4y)(x-y)}{6x(x-y)(x+y)}=\\\\ =\frac{(x^2+xy-4xy-4y^2)-(x^2-xy+4xy-4y^2)}{6x(x^2+xy-xy-y^2)} =\frac{(x^2-3xy-4y^2)-(x^2+3xy-4y^2)}{6x(x^2-y^2)}=\\\\ =\frac{x^2-3xy-4y^2-x^2-3xy+4y^2}{6x(x^2-y^2)}=\frac{-6xy}{6x(x^2-y^2)}=-\frac{y}{x^2-y^2}$