SOLUTION: The problem states to simplify. (3x+3y+3)/9x ÷ (x^2+ 2xy+y^2- 1)/(x^4+ x^2 ) I know you multiply by the reciprocal, but I'm not sure how to get this simplified. Thanks!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The problem states to simplify. (3x+3y+3)/9x ÷ (x^2+ 2xy+y^2- 1)/(x^4+ x^2 ) I know you multiply by the reciprocal, but I'm not sure how to get this simplified. Thanks!      Log On


   

Question 127862This question is from textbook Introductory Algebra
: The problem states to simplify.
(3x+3y+3)/9x ÷ (x^2+ 2xy+y^2- 1)/(x^4+ x^2 )
I know you multiply by the reciprocal, but I'm not sure how to get this simplified. Thanks! This question is from textbook Introductory Algebra

Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
(3x+3y+3)/9x ÷ (x^2+ 2xy+y^2- 1)/(x^4+ x^2 ) =
[(3x+3y+3)/9x] * [(x^4+ x^2 )/(x^2+ 2xy+y^2- 1)] =
(3x+3y+3)*(x^4+ x^2 )/9x*(x^2+ 2xy+y^2- 1)=
(3x+3y+3)(x^3+x)/(9x^2+18xy+9y^2-9)=
(x+y+1)*(x^3+x)/(3x^2+6xy+3y^2-3)