SOLUTION: Please help me simplify with division: {{{(3x+3y+3)/(9x)}}} / {{{(x^2+2xy+y^2-1)/(x^4+x^2)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me simplify with division: {{{(3x+3y+3)/(9x)}}} / {{{(x^2+2xy+y^2-1)/(x^4+x^2)}}}      Log On


   

Question 207462This question is from textbook Introductory Algebra
: Please help me simplify with division:
%283x%2B3y%2B3%29%2F%289x%29 / %28x%5E2%2B2xy%2By%5E2-1%29%2F%28x%5E4%2Bx%5E2%29 This question is from textbook Introductory Algebra

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2B3y%2B3%29%2F%289x%29÷%28x%5E2%2B2xy%2By%5E2-1%29%2F%28x%5E4%2Bx%5E2%29

Invert the second fraction and change the 
division to multiplication:

%28%283x%2B3y%2B3%29%2F%289x%29%29%28%28x%5E4%2Bx%5E2%29%2F%28x%5E2%2B2xy%2By%5E2-1%29%29

Factor 3x%2B3y%2B3 by factoring out 3 and getting 3%28x%2By%2B1%29

Factor x%5E4%2Bx%5E2 by factoring out x%5E2 and getting x%5E2%28x%5E2%2B1%29

Factor x%5E2%2B2xy%2By%5E2-1 
Factor the first three terms as 
%28x%2By%29%5E2-1
and then factor that as the difference of two squares:
%28%28x%2By%29-1%29%28%28x%2By%29%2B1%29
or
%28x%2By-1%29%28x%2By%2B1%29

Now replace each by its factored form:



Cancel the 3 into the 9.



The x in the bottom cancels out the square in the top:



Cancel the %28x%2By%2B1%29's:



All that's left is

%28x%28x%5E2%2B1%29%29%2F%283%28x%2By-1%29%29

You can leave it like that or multiply out, and get

%28x%5E3%2Bx%29%2F%283x%2B3y-3%29

Edwin