Монгол Бодлогын Сан

Заавар: $a^{\frac16}=x$, $b^{\frac16}=y$ орлуулга ашигла.

Бодолт: $a^{\frac16}=x$, $b^{\frac16}=y$ гэвэл \begin{align*} \text{Илэрх.}&=\biggl(\dfrac{3a^{\frac{1}{6}}-2b^{\frac{1}{6}}}{a^{\frac{1}{3}}-b^{\frac{1}{3}}}-\dfrac{3}{a^{\frac{1}{6}}+b^{\frac{1}{6}}}\biggr):\dfrac{a^{\frac{2}{3}}+a^{\frac{1}{3}}b^{\frac{1}{3}}+b^{\frac{2}{3}}}{b^{\frac{5}{6}}}\\ &=\biggl(\dfrac{3x-2y}{x^2-y^2}-\dfrac{3^{\color{red}{(x-y}}}{x+y}\biggr):\dfrac{x^4+x^2y^2+y^4}{y^5}\\ &=\dfrac{3x-2y-3x+3y}{x^2-y^2}\cdot\dfrac{y^5}{x^4+x^2y^2+y^4}\\ &=\dfrac{y^6}{x^6-y^6}=\dfrac{b}{a-b} \end{align*}