Question

(50 PONTOS)

Simplifique a fração, até ficar irredutível :

$\dfrac{x^4+y^4}{(x+y)^4}$

Answer 1

$\mathsf{ \dfrac{x^{4} + y^{4} }{( x + y)^{4} } =} \\ \\ \mathsf{ \dfrac{ x^{4} + y^{4} }{x^{4} + 4 x^{3}y + 6x^{2} y^{2} + 4xy^{3} + y^{4}} = } \\ \\ \mathsf{ \dfrac{ x^{4}}{x^{4} + 4 x^{3}y + 6x^{2} y^{2} + 4xy^{3} + y^{4}} + \dfrac{y^{4}}{x^{4} + 4 x^{3}y + 6x^{2} y^{2} + 4xy^{3} + y^{4}} }$

Answer 2

Olá Thiago,

$\dfrac{ x^{4}+ y^{4} }{(x+y)^{4} } = \dfrac{x^{4}+ y^{2}}{x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4x y^{3} + y^{4} } \\ \\ \\ \dfrac{x^{4} + y^{4}}{x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4x y^{3} + y^{4} } \\ \\ \\ \dfrac{x^{4}}{x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4x y^{3} + y^{4} } + \dfrac{y^{4}}{x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4x y^{3} + y^{4} }$