Performe each of the following 1)x^3+2x^2-x-2/x^2+2x+1÷x^2+3x+2/x^2-1 ?

To perform the given expression, we need to simplify it step by step.

First, let's simplify the numerator and denominator separately:

Numerator:
x^3 + 2x^2 - x - 2

Denominator:
x^2 + 2x + 1 ÷ x^2 + 3x + 2 ÷ x^2 - 1

Next, let's simplify each fraction separately:

Numerator:
x^3 + 2x^2 - x - 2

Denominator:
(x^2 + 2x + 1) ÷ (x^2 + 3x + 2) ÷ (x^2 - 1)

Now, let's simplify each fraction by factoring the denominators:

Numerator:
x^3 + 2x^2 - x - 2

Denominator:
(x + 1)(x + 1) ÷ (x + 2)(x + 1) ÷ (x + 1)(x - 1)

Next, let's cancel out any common factors in the numerator and denominator:

Numerator:
x^3 + 2x^2 - x - 2

Denominator:
(x + 1) ÷ (x + 2) ÷ (x - 1)

Now, let's multiply the fractions by the reciprocal of the denominator:

Numerator:
(x^3 + 2x^2 - x - 2) ÷ (x + 1) ÷ (x + 2) ÷ (x - 1)

Denominator:
1

Finally, let's simplify the expression:

(x^3 + 2x^2 - x - 2) ÷ (x + 1) ÷ (x + 2) ÷ (x - 1)

And that is the simplified expression.