Question

I can't figure out where I'm messing up at. Pic attached.

Answer 1

you want to multiply the numerator of the first expression and second expression
then you want to multiply the denominator of the first and second expressions

Answer 2

1/n^2 Is this answer right?

Answer 3

how so? show me your solution

Answer 4

Does that say?\[\frac{n^5}{n-6}\cdot\frac{n^2-6n}{n^8}\]

Answer 5

yes

Answer 6

Not
\[\frac{n^5}{n-6}=\frac{n^2-6n}{n^8}\]

Answer 7

correct

Answer 8

Here is my work.

Answer 9

@UnknownRandom : I'd strongly suggest not doing the multiplication that you've indicated in your attachment. Here's why:

You can greatly simplify this problem by dividing that n^5 into that n^8; the result will be n^5 where the denominator n^8 is now:\[\frac{ n^5 }{ n-6}*\frac{ n^2-6n }{n ^{8} }\rightarrow \frac{ 1 }{n-6 }*\frac{ n^2-6n }{ n^3 }\]

Answer 10

Note that your new numerator, n^2-6n, can be factored into n(n-6).

Answer 11

So now we have\[\frac{ n(n-6) }{ (n-6) n^3}\]

and this reduces to \[\frac{ 1 }{ n^2 }\]

This is not the fastest or best way to solve reduce this expression in n.

To re-cap; you have nothing to gain from multiplying out numerator and denominator. Instead, factor numerator and denominator and cancel whatever you can. This leads to the proper answer MUCH faster.

Answer 12

Thank you so much @mathmale !

Answer 13

My great pleasure!