Simplify. ((x^4+y^5)(x^4-y^5)+y^10)/(x^8)

To simplify the given expression, we can start by expanding the numerator and then simplify the resulting expression.<br /><br />The numerator is $(x^{4}+y^{5})(x^{4}-y^{5})+y^{10}$. We can use the difference of squares formula to simplify this expression:<br /><br />$(x^{4}+y^{5})(x^{4}-y^{5}) = (x^{4})^{2} - (y^{5})^{2} = x^{8} - y^{10}$<br /><br />So, the numerator becomes $x^{8} - y^{10} + y^{10}$. Simplifying this expression, we get $x^{8}$.<br /><br />Now, we can divide the numerator by the denominator $x^{8}$:<br /><br />$\frac{x^{8}}{x^{8}} = 1$<br /><br />Therefore, the simplified expression is $1$.