Question

Simplify the following expression completely, where x ≠ 0.

Option 1: (x^2 + 3x + 2)/(x + 1).
Option 2: (x - 2)/(x^2 - 1).
Option 3: (x^2 - 4)/(x - 2).
Option 4: (x + 1)/(x^2 - 1

Answer 1

To simplify the expressions completely: Option 1: (x^2 + 3x + 2)/(x + 1) cannot be simplified further. Option 2: (x - 2)/(x^2 - 1) can be simplified to (x - 2)/[(x - 1)(x + 1)]. Option 3: (x^2 - 4)/(x - 2) can be simplified to (x + 2)/(x - 2). Option 4: (x + 1)/(x^2 - 1) can be simplified to 1/(x - 1).

Step-by-step explanation:

To simplify each expression completely:

1. Option 1: (x2 + 3x + 2)/(x + 1)
2. This expression cannot be simplified further as there is no common factor in the numerator and denominator.
3. Option 2: (x - 2)/(x2 - 1)
4. We can factor the denominator as (x - 1)(x + 1). The expression can be simplified to (x - 2)/[(x - 1)(x + 1)].
5. Option 3: (x2 - 4)/(x - 2)
6. We can factor the numerator as (x - 2)(x + 2). The expression can be simplified to (x + 2)/(x - 2).
7. Option 4: (x + 1)/(x2 - 1)
8. We can factor the denominator as (x - 1)(x + 1). The expression can be simplified to (x + 1)/[(x - 1)(x + 1)]. However, since x ≠ 0, we can further simplify it to 1/(x - 1).