# How do you simplify #(a^3 - b^3)/(3a^2 + 9ab + 6b^2)*(a^2 + 2ab + b^2)/(a^2 - b^2)#?

Factor and cancel matching factors to find:

Use difference of cubes identity:

Use difference of squares identity:

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To simplify the expression (a^3 - b^3)/(3a^2 + 9ab + 6b^2)*(a^2 + 2ab + b^2)/(a^2 - b^2), we can factorize the numerator and denominator separately.

The numerator (a^3 - b^3) can be factored using the difference of cubes formula: (a - b)(a^2 + ab + b^2).

The denominator (3a^2 + 9ab + 6b^2) can be factored by finding the common factor of 3: 3(a^2 + 3ab + 2b^2).

The second denominator (a^2 - b^2) is a difference of squares and can be factored as (a + b)(a - b).

Now, we can cancel out common factors between the numerator and denominator. The (a - b) terms cancel out, leaving us with:

(a^2 + ab + b^2)/(3(a^2 + 3ab + 2b^2))*(a + b)/(a - b)

This is the simplified form of the expression.

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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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