Question

Пожалуйста как сократит?

Answer 1

Ответ:

$\dfrac{\sqrt[4]{b}}{(\sqrt[4]{a}+\sqrt[4]{b})(\sqrt{a}+\sqrt{b})}$

Объяснение:

$\dfrac{\sqrt[4]{ab}-\sqrt{b}}{a-b}=\dfrac{(ab)^{\tfrac{1}{4}}-b^{\tfrac{1}{2}}}{(a^{\tfrac{1}{4}})^{4}-(b^{\tfrac{1}{4}})^{4}}=\dfrac{a^{\tfrac{1}{4}} \cdot b^{\tfrac{1}{4}}-b^{\tfrac{2}{4}}}{((a^{\tfrac{1}{4}})^{2}-(b^{\tfrac{1}{4}})^{2})((a^{\tfrac{1}{4}})^{2}+(b^{\tfrac{1}{4}})^{2})}=$

$=\dfrac{b^{\tfrac{1}{4}} \cdot (a^{\tfrac{1}{4}}-b^{\tfrac{1}{4}})}{(a^{\tfrac{1}{4}}-b^{\tfrac{1}{4}})(a^{\tfrac{1}{4}}+b^{\tfrac{1}{4}})((a^{\tfrac{1}{4}})^{2}+(b^{\tfrac{1}{4}})^{2})}=\dfrac{b^{\tfrac{1}{4}}}{(a^{\tfrac{1}{4}}+b^{\tfrac{1}{4}})((a^{\tfrac{1}{4}})^{2}+(b^{\tfrac{1}{4}})^{2})}=$

$=\dfrac{\sqrt[4]{b}}{(\sqrt[4]{a}+\sqrt[4]{b})(\sqrt{a}+\sqrt{b})};$