Упростить выражение. Распишите подробнее.

Решите задачу:

$\frac{y+1}{4y}*(\frac{y}{y+1}-\frac{y^2}{1+2y+y^2})=\frac{(y+1)(\frac{y}{y+1}-\frac{y^2}{1+2y+y^2})}{4y}=\frac{(y+1)(\frac{y}{y+1}-\frac{y^2}{(y+1)(y+1)})}{4y}=$

$=\frac{(y+1)(\frac{y}{y+1}-y^2(y+1)^{-1-1})}{4y}=\frac{(y+1)(\frac{y}{y+1}-y^2(y+1)^{-2})}{4y}=$

$=\frac{y+1}{4y}*(\frac{y(y+1)}{(y+1)^2}-\frac{y^2}{(y+1)})=\frac{y+1}{4y}*\frac{y(y+1)-y^2}{(y+1)^2}=\frac{(y+1)^{1-2}*(y(y+1)-y^2)}{4y}=$

$=\frac{(y+1)^{-1}*(y(y+1)-y^2)}{4y}=\frac{y^2+y-y^2}{4y(y+1)}=\frac{y}{4y(y+1)}=\frac{1}{4(y+1)}$