Question

выполните сложение и вычитание дробей : (х+у)^2/6у+(х-у)^2/12у-x^2-y^2/4y

Answer 1

$\frac{(x+y)^2}{6y}+\frac{(x-y)^2}{12y}-\frac{x^2-y^2}{4y}= \frac{2(x+y)^2}{12y}+\frac{(x-y)^2}{12y}-\frac{3(x^2-y^2)}{12y}= \\ =\frac{2x^2+4xy+2y^2+x^2-2xy+y^2-3x^2+3y^2}{12y}=\frac{6y^2+2xy}{12y}= \frac{2y(3y+x)}{12y}= \\ =\frac{3y+x}{6}$