Question

Сократите дробь. Спасибо огромное!!!

Answer 1

$frac{x+3sqrt{5x}}{x-45}=frac{sqrt{x}cdot (sqrt{x}+3sqrt5)}{(sqrt{x})^2-(3sqrt5)^2}=frac{sqrt{x}cdot (sqrt{x}+3sqrt5)}{(sqrt{x}-3sqrt5)(srqt{x}+3sqrt5)}=frac{sqrt{x}}{sqrt{x}-3sqrt5}\\\frac{sqrt{125a^3}+sqrt{64b^3}}{5a-2sqrt{5ab}+4b}=frac{(sqrt{5a})^3+(sqrt{4b})^3}{(sqrt{5a})^2-2cdot sqrt{5a}cdot sqrt{b}+(2sqrt{b})^2}=frac{(sqrt{5a}+sqrt{4b})(5a-sqrt{5a}cdot sqrt{4b}+4b)}{5a-sqrt{5a}cdot sqrt{4b}+4b}=\\=sqrt{5a}+sqrt{4b}=sqrt{5a}+2sqrt{b}$