SOLUTION: ((x^2-6x+8)/(x^2-2x))/(3x-12) How do you know when to simplify and divide the polynomials, and when to do long division? And the, which do you do first, the sipmlifying or the div

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: ((x^2-6x+8)/(x^2-2x))/(3x-12) How do you know when to simplify and divide the polynomials, and when to do long division? And the, which do you do first, the sipmlifying or the div      Log On


   

Question 32802This question is from textbook Heath Algebra 1 An Integrated Approach
: ((x^2-6x+8)/(x^2-2x))/(3x-12)
How do you know when to simplify and divide the polynomials, and when to do long division? And the, which do you do first, the sipmlifying or the dividing? Truthfully I think i need help with the over all Algebra subject, because i'm doing so well in that class.
Thank you,
J.A. This question is from textbook Heath Algebra 1 An Integrated Approach

Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2-6x%2B8%29%2F%28x%5E2-2x%29%29%2F%283x-12%29
First we begin by simplifying x%5E2-6x%2B8
X%5E2+-4x-2x-8+=+%28X-4%29%28X-2%29
Then X%5E2-+2X we take X common and we get X(X-2)
Similarly for 3X-12 we take 3 common and we get 3(X-4)
Now we know that %28a%2Fb%29%2Fc+=+a%2Fbc
So you get
%28%28X-4%29%28X-2%29%29%2FX%28X-2%293%28X-4%29
Cancelling the common terms you get 1%2F3X as your final answer