How do you simplify #n^5/(n-6) * (n^2-6n)/(n^8)#?

Answer 1

Nathan Axel

#1/n^2#

Note that: #n^5/(n-6)*(n^2-6n)/n^8=n^6/(n-6)(n-6)/n^8#

Cancel similar terms and we have: #n^6/(n-6)(n-6)/n^8=1/n^2#

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Answer 2

Hazel Anglin

To simplify the expression (n^5/(n-6)) * ((n^2-6n)/(n^8)), we can cancel out common factors in the numerator and denominator.

First, let's factorize the expressions: n^5/(n-6) can be written as n^5 / (n(n-6)) (n^2-6n)/(n^8) can be written as (n(n-6))/(n^8)

Now, cancel out the common factors: (n^5 / (n(n-6))) * ((n(n-6))/(n^8)) = (n^5 * n(n-6)) / (n(n-6) * n^8) = (n^6(n-6)) / (n^9(n-6)) = n^6 / (n^9) = 1 / (n^3)

Therefore, the simplified expression is 1 / (n^3).

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Answer from HIX Tutor

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.