Question

Ребят помогите докажите тождество

Answer 1

$(\frac{2y+1}{y^2+6y+9}-\frac{y-2}{y^2+3y}):\frac{y^2+6}{y^3-9y}=\\\\=(\frac{2y+1}{(y+3)^2}-\frac{y-2}{y(y+3)}):\frac{y^2+6}{y^3-9y}=\\\\=\frac{(2y+1)*y-(y-2)*(y+3)}{y*(y+3)^2}:\frac{y^2+6}{y^3-9y}=\\\\=\frac{2y^2+y-(y^2-2y+3y-6)}{y*(y+3)^2}:\frac{y^2+6}{y^3-9y}=\\\\=\frac{2y^2+y-y^2-y+6}{y*(y+3)^2}:\frac{y^2+6}{y^3-9y}=\\\\=\frac{y^2+6}{y*(y+3)^2}:\frac{y^2+6}{y^3-9y}=\\\\=\frac{y^2+6}{y*(y+3)^2}*\frac{y(y^2-9)}{y^2+6}=$

$=\frac{(y^2+6)*y*(y-3)(y+3)}{y*(y+3)^2*(y^2+6)}=\frac{y-3}{y+3}$