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1) ![frac{ sqrt[4]{ a^{3}}- sqrt[4]{a}+ sqrt{a}-1 }{a- sqrt{a} }= frac{ sqrt[4]{a}( sqrt{a}-1)+( sqrt{a}-1 ) }{ sqrt{a}( sqrt{a}-1) }= frac{( sqrt{a}-1)( sqrt[4]{a}+1) }{ sqrt{a}( sqrt{a}-1) }= frac{ sqrt[4]{a}+1 }{ sqrt{a} }](https://tex.z-dn.net/?f=+frac%7B+sqrt%5B4%5D%7B+a%5E%7B3%7D%7D-+sqrt%5B4%5D%7Ba%7D%2B+sqrt%7Ba%7D-1+%7D%7Ba-+sqrt%7Ba%7D+%7D%3D+frac%7B+sqrt%5B4%5D%7Ba%7D%28+sqrt%7Ba%7D-1%29%2B%28+sqrt%7Ba%7D-1+%29++%7D%7B+sqrt%7Ba%7D%28+sqrt%7Ba%7D-1%29++%7D%3D+frac%7B%28+sqrt%7Ba%7D-1%29%28+sqrt%5B4%5D%7Ba%7D%2B1%29++%7D%7B+sqrt%7Ba%7D%28+sqrt%7Ba%7D-1%29++%7D%3D++frac%7B+sqrt%5B4%5D%7Ba%7D%2B1+%7D%7B+sqrt%7Ba%7D+%7D+++++ "frac{ sqrt[4]{ a^{3}}- sqrt[4]{a}+ sqrt{a}-1 }{a- sqrt{a} }= frac{ sqrt[4]{a}( sqrt{a}-1)+( sqrt{a}-1 ) }{ sqrt{a}( sqrt{a}-1) }= frac{( sqrt{a}-1)( sqrt[4]{a}+1) }{ sqrt{a}( sqrt{a}-1) }= frac{ sqrt[4]{a}+1 }{ sqrt{a} }")
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2)![frac{ sqrt[3]{ a^{2} }- sqrt{b} }{ sqrt[3]{a}+ sqrt[4]{b} }= frac{ (sqrt[3]{a}- sqrt[4]{b})( sqrt[3]{a}+ sqrt[4]{b} )}{ sqrt[3]{a}+ sqrt[4]{b}}= sqrt[3]{a}- sqrt[4]{b}](https://tex.z-dn.net/?f=+frac%7B+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D-+sqrt%7Bb%7D++%7D%7B+sqrt%5B3%5D%7Ba%7D%2B+sqrt%5B4%5D%7Bb%7D++%7D%3D+frac%7B+%28sqrt%5B3%5D%7Ba%7D-+sqrt%5B4%5D%7Bb%7D%29%28+sqrt%5B3%5D%7Ba%7D%2B+sqrt%5B4%5D%7Bb%7D+%29%7D%7B+sqrt%5B3%5D%7Ba%7D%2B+sqrt%5B4%5D%7Bb%7D%7D%3D+sqrt%5B3%5D%7Ba%7D-+sqrt%5B4%5D%7Bb%7D++++ "frac{ sqrt[3]{ a^{2} }- sqrt{b} }{ sqrt[3]{a}+ sqrt[4]{b} }= frac{ (sqrt[3]{a}- sqrt[4]{b})( sqrt[3]{a}+ sqrt[4]{b} )}{ sqrt[3]{a}+ sqrt[4]{b}}= sqrt[3]{a}- sqrt[4]{b}")
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3)![frac{ sqrt[9]{ a^{4}}- sqrt[4]{ b^{9} } }{ sqrt[3]{ a^{2} }+ sqrt{ b^{3}}}= frac{( sqrt[3]{ a^{2} }- sqrt{ b^{3} })( sqrt[3]{ a^{2} }+ sqrt{ b^{3} } ) }{ sqrt[3]{ a^{2} }+ sqrt{ b^{3} } }= sqrt[3]{ a^{2} }- sqrt{ b^{3} }](https://tex.z-dn.net/?f=+frac%7B+sqrt%5B9%5D%7B+a%5E%7B4%7D%7D-+sqrt%5B4%5D%7B+b%5E%7B9%7D+%7D++%7D%7B+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D%2B+sqrt%7B+b%5E%7B3%7D%7D%7D%3D+frac%7B%28+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D-+sqrt%7B+b%5E%7B3%7D+%7D%29%28+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D%2B+sqrt%7B+b%5E%7B3%7D+%7D+%29+%7D%7B+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D%2B+sqrt%7B+b%5E%7B3%7D+%7D++%7D%3D+sqrt%5B3%5D%7B+a%5E%7B2%7D+%7D-+sqrt%7B+b%5E%7B3%7D+%7D+++++ "frac{ sqrt[9]{ a^{4}}- sqrt[4]{ b^{9} } }{ sqrt[3]{ a^{2} }+ sqrt{ b^{3}}}= frac{( sqrt[3]{ a^{2} }- sqrt{ b^{3} })( sqrt[3]{ a^{2} }+ sqrt{ b^{3} } ) }{ sqrt[3]{ a^{2} }+ sqrt{ b^{3} } }= sqrt[3]{ a^{2} }- sqrt{ b^{3} }")
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Большое спасибо
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