Question

División algebraica, es muy importante entregarlo por eso doy tantos puntos.

Answer 1

Factorizamos por x² en ambas expresiones:

$\frac{x^{2}(x^{10}+x^{4}y^{6}-x^{6}y^{4}-y^{10})}{x^{2}(x^{6}+x^{4}y^{2}-x^{2}y^{4}-y^{6})}$

Simplificamos los x² y nos queda:

$\frac{x^{10}+x^{4}y^{6}-x^{6}y^{4}-y^{10}}{x^{6}+x^{4}y^{2}-x^{2}y^{4}-y^{6}} \\\\\frac{x^{4}(x^{6}+y^{6})-y^{4}(x^{6}+y^{6})}{x^{4}(x^{2}+y^{2})-y^{4}(x^{2}+y^{2})}\\\\\frac{(x^{6}+y^{6})(x^{4}-y^{4})}{(x^{2}+y^{2})(x^{4}-y^{4})}\\\\Simplificamos\\\\ \frac{(x^{6}+y^{6})}{(x^{2}+y^{2})} \\\\\frac{(x^{2}+y^{2})(x^{4}-x^{2}y^{2}+y^{4})}{(x^{2}+y^{2})}\\\\Simplificamos\\\\(x^{4}-x^{2}y^{2}+y^{4})$