Verified answer

[tex]\displaystyle\bf\\\frac{a^{2}-y^{2} +2a-2y }{(a+y+2)^{2} }=\frac{(a^{2}-y^{2} )+(2a-2y) }{(a+y+2)^{2} } =\frac{(a-y)(a+y)+2(a-y)}{(a+y+2)^{2} }=\\\\\\=\frac{(a-y)(a+y+2)}{(a+y+2)^{2} } =\frac{a-y}{a+y+2}[/tex]