(a-1+2/a+1)/a^2+1/а^2+2а+1

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To simplify this expression, we first need to combine the terms in the numerator:

(a - 1 + 2/(a + 1))/(a^2 + 1/а^2 + 2а + 1)

= ((a^2 + a - a + 1 + 2)/(a + 1))/(a^2 + a/а^2 + 2а + 1)

= ((a^2 + 1 + 2)/(a + 1))/(a^2 + 1 + 2а + 1)

= ((a^2 + 3)/(a + 1))/(a^2 + 2а + 2)

Now, we need to factor the denominators:

a^2 + 3 = (a + √3)(a - √3)
a^2 + 2a + 2 = (a + 1 + √3i)(a + 1 - √3i)

Therefore, the expression simplifies to:

((a + √3)(a - √3))/((a + 1 + √3i)(a + 1 - √3i))

This is the simplified form of the given expression.