SOLUTION: this is a problem that I have been trying to figure out for my homework and just cant get it. Any help would be appreciated Simplify(3x+3y+3)/9x÷(x^2+2xy+y^2-1)/(x^4+x^2 )

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: this is a problem that I have been trying to figure out for my homework and just cant get it. Any help would be appreciated Simplify(3x+3y+3)/9x÷(x^2+2xy+y^2-1)/(x^4+x^2 )      Log On


   

Question 272608: this is a problem that I have been trying to figure out for my homework and just cant get it. Any help would be appreciated
Simplify(3x+3y+3)/9x÷(x^2+2xy+y^2-1)/(x^4+x^2 )
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
(3x+3y+3)/9x ÷ (x^2+2xy+y^2-1)/(x^4+x^2 )
----
[3(x+y+1)]/[9x] + [(x+y)^2-1]/[x^2(x^2+1)]
----
[x+y+1)]/[3x] + [(x+y)^2-1]/[x^2(x^2+1)]
---------
[x+y+1]/[3x] + [(x+y+1)(x+y-1)]/[x^2(x^2+1)]
------------------
[1]/[3x] + [(x+y-1)]/[x^2(x^2+1)]
------------------
gcd = 3x^2(x^2+1)
------------------
[x(x^2+1)/gcd] + [3(x+y-1)/gcd]
-----------------
[x^3+x+3x+3y-3]/gcd
------------------------
[x^3+4x+3y-3]/[3x^2(x^2+1)]
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Cheers,
Stan H.