How to Simplify This Algebraic Expression?

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The discussion focuses on simplifying the algebraic expression (x^4 + x^2y^2 + y^4)/(x^2 - x^2y^2 + y^2). A participant confirms the correctness of the denominator, which leads to confusion among others about the simplification process. Some suggest trying division as a method to simplify the expression. Clarification and further elaboration on the steps involved in the simplification are requested. The conversation highlights the challenges faced when tackling complex algebraic expressions.
Jahnabi
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Hey!

Can anybody help me with this?

I need to simply the following expression:

(x^4 + x^2y^2 + y^4)/(x^2 - x^2y^2 + y^2)

I'd be so thankful ..
 
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Jahnabi said:
Hey!

Can anybody help me with this?

I need to simply the following expression:

(x^4 + x^2y^2 + y^4)/(x^2 - x^2y^2 + y^2)

I'd be so thankful ..

are sure the expression in the denominator is x^2 - x^2y^2 + y^2 and not x^2 - xy + y^2
 
yeah ..

oh, yeah .. I'm very sure about that ..
 
GroebnerBasis

hope it helps
 

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I'm sorry, but that went right over me ..! I didn't understand it a little bit .. Could you kindly elaborate? I'd be so very thankful ..
 
Did you simply try dividing?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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