# How do you divide #{(n^2-n-12)/(2n^2-15n+18)}/{(3n^2-12n)/(2n^3-9n^2)}#?

For solving the above we need to factorize each polynomial.

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To divide the given expression, we can simplify it by multiplying the numerator by the reciprocal of the denominator. This can be done as follows:

(n^2 - n - 12) / (2n^2 - 15n + 18) divided by (3n^2 - 12n) / (2n^3 - 9n^2)

Dividing is equivalent to multiplying by the reciprocal, so we can rewrite the expression as:

(n^2 - n - 12) / (2n^2 - 15n + 18) * (2n^3 - 9n^2) / (3n^2 - 12n)

Next, we can simplify the expression by canceling out common factors:

(n^2 - n - 12) * (2n^3 - 9n^2) / (2n^2 - 15n + 18) * (3n^2 - 12n)

Expanding and combining like terms in the numerator and denominator:

(2n^5 - 9n^4 - 2n^4 + 9n^3 - 36n^3 + 162n^2 - 3n^3 + 13n^2 + 36n^2 - 162n - 36n + 162) / (6n^4 - 24n^3 + 27n^2 - 24n^3 + 96n^2 - 108n)

Simplifying further:

(2n^5 - 11n^4 - 30n^3 + 211n^2 - 198n + 162) / (6n^4 - 48n^3 + 123n^2 - 108n)

Therefore, the division of the given expression is:

(2n^5 - 11n^4 - 30n^3 + 211n^2 - 198n + 162) / (6n^4 - 48n^3 + 123n^2 - 108n)

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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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