[tex]\frac{x^{4m}-y^{4n}}{x^{3m}+x^{2m}y^{n}+x^{m}y^{2n}+y^{3n}}\\\\ =\frac{(x^{2m}-y^{2n}).(x^{2m}+y^{2n})}{(x^{m}+y^{n}).(x^{2m}-x^{m}y^{n}+y^{2n})+x^{m}y^{n}.(x^{m}+y^{n})}\\\\ =\frac{(x^{m}-y^{n})(x^{m}+y^{n}).(x^{2m}+y^{2n})}{(x^{m}+y^{n}).(x^{2m}+y^{2n})}\\\\ =x^{m}-y^{n}[/tex]