0} \atop {\sqrt{x}-\sqrt[3]{x}\ne 0}} \right. \; \left \{ {{x>0} \atop {\sqrt{x}\ne \sqrt[3]{x}}} \right. \; \left \{ {{x>0} \atop {x\ne 1}} \right. \\\\\sqrt{x}+\sqrt[3]{x}=3\sqrt{x}-3\sqrt[3]{x}\\\\2\sqrt{x}-4\sqrt[3]{x}=0\\\\2(\sqrt{x}-2\sqrt[3]{x})=0\\\\\sqrt[3]{x}(\sqrt[6]{x}-2)=0\\\\1)\; \sqrt[3]{x}=0\; \; \; \; ili\; \; \; 2)\; \; \sqrt[6]{x}=2\\\\x=0\; \notin OOF\; \; \; ili\; \; \; x=2^6=64 " alt="\frac{\sqrt{x}+\sqrt[3]{x}}{\sqrt{x}-\sqrt[3]{x}}=3,\; \; OOF:\; \left \{ {{x>0} \atop {\sqrt{x}-\sqrt[3]{x}\ne 0}} \right. \; \left \{ {{x>0} \atop {\sqrt{x}\ne \sqrt[3]{x}}} \right. \; \left \{ {{x>0} \atop {x\ne 1}} \right. \\\\\sqrt{x}+\sqrt[3]{x}=3\sqrt{x}-3\sqrt[3]{x}\\\\2\sqrt{x}-4\sqrt[3]{x}=0\\\\2(\sqrt{x}-2\sqrt[3]{x})=0\\\\\sqrt[3]{x}(\sqrt[6]{x}-2)=0\\\\1)\; \sqrt[3]{x}=0\; \; \; \; ili\; \; \; 2)\; \; \sqrt[6]{x}=2\\\\x=0\; \notin OOF\; \; \; ili\; \; \; x=2^6=64 " align="absmiddle" class="latex-formula">
Ответ: x=64