# How do you find the domain for #f(x) = (4x^2 - 9)/(x^2 + 5x + 6)#?

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To find the domain of the function f(x) = (4x^2 - 9)/(x^2 + 5x + 6), we need to determine the values of x for which the function is defined.

The function is defined for all real numbers except the values that make the denominator equal to zero.

To find these values, we set the denominator equal to zero and solve for x:

x^2 + 5x + 6 = 0

Factoring the quadratic equation, we have:

(x + 2)(x + 3) = 0

Setting each factor equal to zero, we get:

x + 2 = 0 or x + 3 = 0

Solving these equations, we find:

x = -2 or x = -3

Therefore, the domain of the function f(x) is all real numbers except x = -2 and x = -3.

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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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