[1/(a-2)+a/(a²+a-2)]÷(a/a+2)²
=[(1/a-2)+(a+a-2)]÷(1+2)²
=[(1/a-2)+(2a-2)]÷9
=[(1/a-2)+2a-2]÷9
=[(1/a-2)+(1/2a)-2] ÷9
=[(1/a-2)+(a-2/2a×(a-2)-2] ÷9
=[(1/a-2)+(a-2/2a×a-4a)-2]÷9
=1+2a×-4a/9a-18
[1/(a-2)+a/(a²+a-2)]÷(a/a+2)²
=[(1/a-2)+(a+a-2)]÷(1+2)²
=[(1/a-2)+(2a-2)]÷9
=[(1/a-2)+2a-2]÷9
=[(1/a-2)+(1/2a)-2] ÷9
=[(1/a-2)+(a-2/2a×(a-2)-2] ÷9
=[(1/a-2)+(a-2/2a×a-4a)-2]÷9
=1+2a×-4a/9a-18