Respuesta :

[tex]:\implies\sf\:\dfrac{4a^3}{a^4+x^4}+\dfrac{8a^7}{x^8-a^8}[/tex]

[tex]:\implies\sf\:\dfrac{4a^3(x^8-a^8)+8a^7(a^4+x^4)}{(a^4+x^4)(x^4-a^4)(x^4+a^4)}[/tex]

[tex]:\implies\sf\:\dfrac{4a^3x^8-4a^{11}+8a^{11}+8a^7x^4}{(a^4+x^4)^2(x^4-a^4)}[/tex]

[tex]:\implies\sf\:\dfrac{4a^3x^8+4a^{11}+8a^7x^4}{(a^4+x^4)^2(x^4-a^4)}[/tex]

[tex]:\implies\sf\:\dfrac{4a^3(a^8+2a^4x^4+x^8)}{(a^4+x^4)^2(x^4-a^4)}[/tex]

[tex]:\implies\sf\:\dfrac{4a^3\tt{(a^4+x^4)^2}}{{\tt(a^4+x^4)^2}(x^4-a^4)}[/tex]

[tex]:\implies\boxed{\bf{\purple{\dfrac{4a^3}{(x^4-a^4)}}}}[/tex]

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