How do you divide #(x^3+27)/(9x+27) div(3x^29x+27)/(4x)#?
...using the sum of cubes identity
So:
Then the numerator of the second factor is
So we have:
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To divide (x^3+27)/(9x+27) by (3x^29x+27)/(4x), we can follow these steps:

Factorize the numerator and denominator of both fractions, if possible. (x^3+27) can be factored as (x+3)(x^23x+9). (9x+27) can be factored as 9(x+3). (3x^29x+27) can be factored as 3(x^23x+9). (4x) can be factored as 4(x).

Rewrite the division as multiplication by the reciprocal of the second fraction. (x^3+27)/(9x+27) * (4x)/(3x^29x+27)

Cancel out any common factors between the numerators and denominators. (x+3) cancels out in the numerator and denominator.

Multiply the remaining factors together. (x^23x+9) * (4x) / (9 * 3(x^23x+9))

Simplify the expression. (4x(x^23x+9)) / (27(x^23x+9))

Cancel out any common factors between the numerator and denominator. (x^23x+9) cancels out.

The final result is: 4x / 27
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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