# How do you simplify and restricted value of #(x^3 - 2x + 3)/( x^2 + 12x + 32)#?

Let's factorise the denominator using the "middle-term break":

The denominator of the fraction can never equal to zero:

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To simplify the expression (x^3 - 2x + 3)/(x^2 + 12x + 32), we can factor the numerator and denominator. The numerator can be factored as (x - 1)(x^2 + x - 3), and the denominator can be factored as (x + 4)(x + 8).

Therefore, the expression can be simplified as (x - 1)(x^2 + x - 3)/(x + 4)(x + 8).

To find the restricted values, we need to identify the values of x that would make the denominator equal to zero. In this case, the restricted values are x = -4 and x = -8, as they would make the denominator (x + 4)(x + 8) equal to zero.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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