Kết quả rút gọn của biều thức fracsqrt3a4+sqrt3a2 b2+sqrt3b5sqrt3a2+sqrt3a

Ta có

$\frac{\sqrt[3]{a^{4}}+\sqrt[3]{a^{2} b^{2}}+\sqrt[3]{b^{4}}}{\sqrt[3]{a^{2}}+\sqrt[3]{a b}+\sqrt[3]{b^{2}}}=\frac{\left(\sqrt[3]{a^{2}}-\sqrt[3]{b^{2}}\right)\left(\sqrt[3]{a^{4}}+\sqrt[3]{a^{2} b^{2}}+\sqrt[3]{b^{4}}\right)}{\left(\sqrt[3]{a^{2}}-\sqrt[3]{b^{2}}\right)\left(\sqrt[3]{a^{2}}+\sqrt[3]{a b}+\sqrt[3]{b^{2}}\right)}$

$=\frac{\left(\sqrt[3]{a^{2}}\right)^{3}-\left(\sqrt[3]{b^{2}}\right)^{3}}{(\sqrt[3]{a}+\sqrt[3]{b})(\sqrt[3]{a}-\sqrt[3]{b}) \cdot\left(\sqrt[3]{a^{2}}+\sqrt[3]{a b}+\sqrt[3]{b^{2}}\right)}$

$=\frac{\left(\sqrt[3]{a^{2}}\right)^{3}-\left(\sqrt[3]{b^{2}}\right)^{3}}{(\sqrt[3]{a}+\sqrt[3]{b})\left(\sqrt[3]{a^{3}}-\sqrt[3]{b^{3}}\right)}=\frac{a^{2}-b^{2}}{(\sqrt[3]{a}+\sqrt[3]{b}) \cdot(a-b)}$

$=\frac{(a+b) \cdot(a-b)}{(\sqrt[3]{a}+\sqrt[3]{b}) \cdot(a-b)}=\frac{a+b}{\sqrt[3]{a}+\sqrt[3]{b}}$

$=\frac{(\sqrt[3]{a}+\sqrt[3]{b}) \cdot\left(\sqrt[3]{a^{2}}-\sqrt[3]{a b}+\sqrt[3]{b^{2}}\right)}{\sqrt[3]{a}+\sqrt[3]{b}}$

$=\sqrt[3]{a^{2}}-\sqrt[3]{a b}+\sqrt[3]{b^{2}}$