Question

Упростить:
$frac{ a^{1,5} - x^{1,5}}{ a^{0,5} - x^{0,5} }$

Answer 1

$frac{a^{1,5}-x^{1,5}}{a^{0,5}-x^{0,5}}= frac{(a^{0,5})^3-(x^{0,5})^3}{a^{0,5}-x^{0,5}}= frac{(a^{0,5}-x^{0,5})(a+a^{0,5}x^{0,5}+x)}{a^{0,5}-x^{0,5}}=a+a^{0,5}x^{0,5}+x=\\=a+x+ sqrt{ax}$