Firejay5
  • Firejay5
Simplify. Show work and explain. 13. n^5 over n - 6 * n^2 - 6n over n^8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Mertsj
  • Mertsj
Factor 3y^2 out of the numerator
Mertsj
  • Mertsj
Awesome!!
Mertsj
  • Mertsj
Remember to multiply by the reciprocal and factor n^2-6n by factoring out n

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More answers

Firejay5
  • Firejay5
cancel out n - 6
Mertsj
  • Mertsj
yes
Firejay5
  • Firejay5
so now we have n^5 * n over n^8
Mertsj
  • Mertsj
no
Firejay5
  • Firejay5
what do you mean
Mertsj
  • Mertsj
\[\frac{n^5}{n-6}\times\frac{n(n-6)}{n^8}=\frac{1}{n^2}\]
Firejay5
  • Firejay5
@abb0t
abb0t
  • abb0t
?
Firejay5
  • Firejay5
I need someone to finish Mertsj's work
zepdrix
  • zepdrix
\[\large \frac{n^5}{n-6}\times \frac{n^2-6n}{n^8}\] Hmm do you understand what he did so far? That was a bunch of steps all done at once, I can understand if it was a little confusing.
Firejay5
  • Firejay5
I understand that, but I need the explanation of how that = 1 over n^2
zepdrix
  • zepdrix
\[\large \frac{n^5}{n-6}\times \frac{\color{orangered}{n^2-6n}}{n^8}\] For this orange part, factor an n out of each term.\[\large \frac{n^5}{n-6}\times \frac{\color{orangered}{n(n-6)}}{n^8}\]
zepdrix
  • zepdrix
From here we'll simply multiply across, Put brackets around the n-6 on the bottom, so the multiplication is a little clearer.\[\large \frac{n^5}{(n-6)}\times \frac{n(n-6)}{n^8}\] Then multiplying across gives us,\[\large \frac{n^5\times n(n-6)}{n^8(n-6)} \qquad = \qquad \frac{n^6(n-6)}{n^8(n-6)}\]Understand so far? :o
Firejay5
  • Firejay5
yes
zepdrix
  • zepdrix
The n-6's can divide out,\[\large \frac{n^6\cancel{(n-6)}}{n^8\cancel{(n-6)}} \qquad = \qquad \frac{n^6}{n^8}\]
zepdrix
  • zepdrix
From here, we want to remember our rules for exponents. When we divide terms of the same base, we `subtract` the exponents.\[\large \frac{n^6}{n^8} \qquad = \qquad n^{6-8}\]
Firejay5
  • Firejay5
then's it's 1 over n^2
zepdrix
  • zepdrix
\[\large n^{-2}\qquad = \qquad \frac{1}{n^2}\]Yes :)
Firejay5
  • Firejay5
you can do that OR the biggest exponent is on the bottom <--- 8 - 6 = 2
Firejay5
  • Firejay5
substract

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