¿Me podrían explicar como se hace esto? Por favor.
Y si me pueden dar un ejemplo de estas me ayudarían bastante.:((
Adjuntos:
![](https://es-static.z-dn.net/files/d41/ecb41dd8117ff1dbebae7430f101aca5.jpg)
![](https://es-static.z-dn.net/files/d98/2429a028ed4af8458679f057519ea584.jpg)
Respuestas a la pregunta
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Hola!
Vamos analizar cada uno para que puedas ver los conceptos
![a= \dfrac{3}{5}\qquad b= \sqrt{2}\qquad c= 7 \qquad d= \dfrac{6}{5}\qquad e= \sqrt{3} \\ \\ Encuentra \\ \\ a) a+b+c+d+e= \\ \\ \\ \dfrac{3}{5} + \sqrt{2}+ 7+ \dfrac{6}{5} + \sqrt{3}= \dfrac{3+7*5+6}{5} + \sqrt{2} + \sqrt{3}= \boxed{\dfrac{44}{5} + \sqrt{2} + \sqrt{3}} \\ \\ Las \ raices \ quedan \ expresadas. \\ \\ \\ b) \dfrac{a-b}{c+d} = \dfrac{ \frac{3}{5} - \sqrt{2} }{7+ \frac{6}{5} }= \dfrac{ \frac{3}{5} - \sqrt{2} }{ \frac{35+6}{5} }= a= \dfrac{3}{5}\qquad b= \sqrt{2}\qquad c= 7 \qquad d= \dfrac{6}{5}\qquad e= \sqrt{3} \\ \\ Encuentra \\ \\ a) a+b+c+d+e= \\ \\ \\ \dfrac{3}{5} + \sqrt{2}+ 7+ \dfrac{6}{5} + \sqrt{3}= \dfrac{3+7*5+6}{5} + \sqrt{2} + \sqrt{3}= \boxed{\dfrac{44}{5} + \sqrt{2} + \sqrt{3}} \\ \\ Las \ raices \ quedan \ expresadas. \\ \\ \\ b) \dfrac{a-b}{c+d} = \dfrac{ \frac{3}{5} - \sqrt{2} }{7+ \frac{6}{5} }= \dfrac{ \frac{3}{5} - \sqrt{2} }{ \frac{35+6}{5} }=](https://tex.z-dn.net/?f=a%3D++%5Cdfrac%7B3%7D%7B5%7D%5Cqquad+b%3D++%5Csqrt%7B2%7D%5Cqquad+c%3D+7+%5Cqquad+d%3D++%5Cdfrac%7B6%7D%7B5%7D%5Cqquad+e%3D++++%5Csqrt%7B3%7D+++%5C%5C++%5C%5C+Encuentra++%5C%5C++%5C%5C+a%29+a%2Bb%2Bc%2Bd%2Be%3D++%5C%5C++%5C%5C++%5C%5C++%5Cdfrac%7B3%7D%7B5%7D+%2B++%5Csqrt%7B2%7D%2B+7%2B++%5Cdfrac%7B6%7D%7B5%7D+%2B+++%5Csqrt%7B3%7D%3D+%5Cdfrac%7B3%2B7%2A5%2B6%7D%7B5%7D+%2B++%5Csqrt%7B2%7D+%2B+++%5Csqrt%7B3%7D%3D++%5Cboxed%7B%5Cdfrac%7B44%7D%7B5%7D+%2B++%5Csqrt%7B2%7D+%2B+++%5Csqrt%7B3%7D%7D++%5C%5C++%5C%5C+Las+%5C+raices+%5C+quedan+%5C+expresadas.+%5C%5C++%5C%5C++%5C%5C++b%29++%5Cdfrac%7Ba-b%7D%7Bc%2Bd%7D+%3D++%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D+-+%5Csqrt%7B2%7D+%7D%7B7%2B+%5Cfrac%7B6%7D%7B5%7D+%7D%3D++%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D+-+%5Csqrt%7B2%7D+%7D%7B+%5Cfrac%7B35%2B6%7D%7B5%7D+%7D%3D+)
![\dfrac{ \frac{3}{5} - \sqrt{2} }{ \frac{41}{5} }= \dfrac{ \frac{3}{5} }{ \frac{41}{5} }-\dfrac{ 1 }{ \frac{41}{5} } \sqrt{2} = \boxed{ \dfrac{3 }{41 }-\dfrac{ 5 }{41 } \sqrt{2} } \quad la \ raiz \ se \ deja \ expresada \dfrac{ \frac{3}{5} - \sqrt{2} }{ \frac{41}{5} }= \dfrac{ \frac{3}{5} }{ \frac{41}{5} }-\dfrac{ 1 }{ \frac{41}{5} } \sqrt{2} = \boxed{ \dfrac{3 }{41 }-\dfrac{ 5 }{41 } \sqrt{2} } \quad la \ raiz \ se \ deja \ expresada](https://tex.z-dn.net/?f=%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D+-+%5Csqrt%7B2%7D+%7D%7B+%5Cfrac%7B41%7D%7B5%7D+%7D%3D+%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D++%7D%7B+%5Cfrac%7B41%7D%7B5%7D+%7D-%5Cdfrac%7B+1+%7D%7B+%5Cfrac%7B41%7D%7B5%7D+%7D+%5Csqrt%7B2%7D+%3D++%5Cboxed%7B++%5Cdfrac%7B3++%7D%7B41+%7D-%5Cdfrac%7B+5+%7D%7B41+%7D+%5Csqrt%7B2%7D++%7D+%5Cquad+la+%5C+raiz+%5C+se+%5C+deja+%5C+expresada)
![c) \dfrac{d+b+e}{b}= \dfrac{ \frac{6}{5}+ \sqrt{2} + \sqrt{3}}{ \sqrt{2} }\qquad debemos \ racionalizar \\ \\ \\ \dfrac{ \frac{6}{5}+ \sqrt{2} + \sqrt{3}}{ \sqrt{2} }* \dfrac{\sqrt{2}}{ \sqrt{2} }= \qquad sacamos \ la \ taiz \ del \ denominador \\ \\ \\ \dfrac{ \frac{6}{5}* \sqrt{2} + \sqrt{2}^2 + \sqrt{3} *\sqrt{2} }{ \sqrt{2}^2 }=\qquad aplicamos \ distributiva \\ \\ \\ \dfrac{ \frac{6}{5}* \sqrt{2} + 2 + \sqrt{6} }{2 }=\qquad ahora\ resolvemos c) \dfrac{d+b+e}{b}= \dfrac{ \frac{6}{5}+ \sqrt{2} + \sqrt{3}}{ \sqrt{2} }\qquad debemos \ racionalizar \\ \\ \\ \dfrac{ \frac{6}{5}+ \sqrt{2} + \sqrt{3}}{ \sqrt{2} }* \dfrac{\sqrt{2}}{ \sqrt{2} }= \qquad sacamos \ la \ taiz \ del \ denominador \\ \\ \\ \dfrac{ \frac{6}{5}* \sqrt{2} + \sqrt{2}^2 + \sqrt{3} *\sqrt{2} }{ \sqrt{2}^2 }=\qquad aplicamos \ distributiva \\ \\ \\ \dfrac{ \frac{6}{5}* \sqrt{2} + 2 + \sqrt{6} }{2 }=\qquad ahora\ resolvemos](https://tex.z-dn.net/?f=c%29++%5Cdfrac%7Bd%2Bb%2Be%7D%7Bb%7D%3D++%5Cdfrac%7B+%5Cfrac%7B6%7D%7B5%7D%2B+%5Csqrt%7B2%7D+%2B+%5Csqrt%7B3%7D%7D%7B+%5Csqrt%7B2%7D+%7D%5Cqquad+debemos+%5C+racionalizar+%5C%5C++%5C%5C++%5C%5C+++%5Cdfrac%7B+%5Cfrac%7B6%7D%7B5%7D%2B+%5Csqrt%7B2%7D+%2B+%5Csqrt%7B3%7D%7D%7B+%5Csqrt%7B2%7D+%7D%2A+%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B+%5Csqrt%7B2%7D+%7D%3D+%5Cqquad+sacamos+%5C+la+%5C+taiz+%5C+del+%5C+denominador++%5C%5C++%5C%5C++%5C%5C+%5Cdfrac%7B+%5Cfrac%7B6%7D%7B5%7D%2A+%5Csqrt%7B2%7D+%2B+%5Csqrt%7B2%7D%5E2+%2B+%5Csqrt%7B3%7D+%2A%5Csqrt%7B2%7D+%7D%7B+%5Csqrt%7B2%7D%5E2+%7D%3D%5Cqquad+aplicamos+%5C+distributiva+%5C%5C++%5C%5C++%5C%5C+%5Cdfrac%7B+%5Cfrac%7B6%7D%7B5%7D%2A+%5Csqrt%7B2%7D+%2B+2+%2B+%5Csqrt%7B6%7D+%7D%7B2+%7D%3D%5Cqquad+ahora%5C+resolvemos)
![\dfrac{ \frac{6}{5}* \sqrt{2} }{2 }+ \dfrac{ 2 }{2 }+ \dfrac{ \sqrt{6} }{2 }= \boxed{ \dfrac{ 3 }{5 } \sqrt{2} + 1+ \dfrac{1 }{2 } \sqrt{6}} \dfrac{ \frac{6}{5}* \sqrt{2} }{2 }+ \dfrac{ 2 }{2 }+ \dfrac{ \sqrt{6} }{2 }= \boxed{ \dfrac{ 3 }{5 } \sqrt{2} + 1+ \dfrac{1 }{2 } \sqrt{6}}](https://tex.z-dn.net/?f=%5Cdfrac%7B+%5Cfrac%7B6%7D%7B5%7D%2A+%5Csqrt%7B2%7D++%7D%7B2+%7D%2B+%5Cdfrac%7B+2++%7D%7B2+%7D%2B+%5Cdfrac%7B+%5Csqrt%7B6%7D+%7D%7B2+%7D%3D+%5Cboxed%7B+%5Cdfrac%7B+3+++%7D%7B5+%7D+%5Csqrt%7B2%7D+%2B+1%2B+%5Cdfrac%7B1+%7D%7B2+%7D+%5Csqrt%7B6%7D%7D)
![d) \dfrac{a-c-e}{d}= \dfrac{ \frac{3}{5}-7- \sqrt{3} }{ \frac{6}{5}}\qquad \ distribuimos \ el \ denominador \\ \\ \\ \dfrac{ \frac{3}{5} }{ \frac{6}{5}}- \dfrac{7 }{ \frac{6}{5}}- \dfrac{ \sqrt{3} }{ \frac{6}{5}}= \\ \\ \\ \dfrac{ 1 }{2}- \dfrac{35}{ 6}- \dfrac{5 }{ 6} \sqrt{3} = \dfrac{1*3-35}{ 6}- \dfrac{5 }{ 6} \sqrt{3} = \boxed{- \dfrac{16}{3}- \dfrac{5 }{ 6} \sqrt{3}} d) \dfrac{a-c-e}{d}= \dfrac{ \frac{3}{5}-7- \sqrt{3} }{ \frac{6}{5}}\qquad \ distribuimos \ el \ denominador \\ \\ \\ \dfrac{ \frac{3}{5} }{ \frac{6}{5}}- \dfrac{7 }{ \frac{6}{5}}- \dfrac{ \sqrt{3} }{ \frac{6}{5}}= \\ \\ \\ \dfrac{ 1 }{2}- \dfrac{35}{ 6}- \dfrac{5 }{ 6} \sqrt{3} = \dfrac{1*3-35}{ 6}- \dfrac{5 }{ 6} \sqrt{3} = \boxed{- \dfrac{16}{3}- \dfrac{5 }{ 6} \sqrt{3}}](https://tex.z-dn.net/?f=d%29++%5Cdfrac%7Ba-c-e%7D%7Bd%7D%3D+++%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D-7-+%5Csqrt%7B3%7D+%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D%5Cqquad+%5C+distribuimos+%5C+el+%5C+denominador+%5C%5C++%5C%5C++%5C%5C++%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D+%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D-++%5Cdfrac%7B7+%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D-++%5Cdfrac%7B+%5Csqrt%7B3%7D+%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D%3D++%5C%5C++%5C%5C++%5C%5C+%5Cdfrac%7B+1+%7D%7B2%7D-++%5Cdfrac%7B35%7D%7B+6%7D-++%5Cdfrac%7B5+%7D%7B+6%7D+%5Csqrt%7B3%7D+%3D++%5Cdfrac%7B1%2A3-35%7D%7B+6%7D-++%5Cdfrac%7B5+%7D%7B+6%7D+%5Csqrt%7B3%7D+%3D+%5Cboxed%7B-++%5Cdfrac%7B16%7D%7B3%7D-++%5Cdfrac%7B5+%7D%7B+6%7D+%5Csqrt%7B3%7D%7D+)
![e) \dfrac{ab+ce}{d}= \dfrac{ \frac{3}{5}* \sqrt{2}+7* \sqrt{3}}{ \frac{6}{5}}= \\ \\ \\ \dfrac{ \frac{3}{5}* \sqrt{2}}{ \frac{6}{5}}+\dfrac{7* \sqrt{3}}{ \frac{6}{5}} = \\ \\ \\ \dfrac{ \frac{3}{5}}{ \frac{6}{5}} \sqrt{2} +\dfrac{7}{ \frac{6}{5}} \sqrt{3} = \boxed { \frac{1}{2} \sqrt{2}+ \frac{35}{6} \sqrt{3}} e) \dfrac{ab+ce}{d}= \dfrac{ \frac{3}{5}* \sqrt{2}+7* \sqrt{3}}{ \frac{6}{5}}= \\ \\ \\ \dfrac{ \frac{3}{5}* \sqrt{2}}{ \frac{6}{5}}+\dfrac{7* \sqrt{3}}{ \frac{6}{5}} = \\ \\ \\ \dfrac{ \frac{3}{5}}{ \frac{6}{5}} \sqrt{2} +\dfrac{7}{ \frac{6}{5}} \sqrt{3} = \boxed { \frac{1}{2} \sqrt{2}+ \frac{35}{6} \sqrt{3}}](https://tex.z-dn.net/?f=e%29++%5Cdfrac%7Bab%2Bce%7D%7Bd%7D%3D+%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D%2A+%5Csqrt%7B2%7D%2B7%2A+%5Csqrt%7B3%7D%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D%3D++%5C%5C++%5C%5C++%5C%5C+%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D%2A+%5Csqrt%7B2%7D%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D%2B%5Cdfrac%7B7%2A+%5Csqrt%7B3%7D%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D+%3D++%5C%5C++%5C%5C++%5C%5C+%5Cdfrac%7B+%5Cfrac%7B3%7D%7B5%7D%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D+%5Csqrt%7B2%7D+%2B%5Cdfrac%7B7%7D%7B+%5Cfrac%7B6%7D%7B5%7D%7D++%5Csqrt%7B3%7D+%3D++%5Cboxed+%7B+%5Cfrac%7B1%7D%7B2%7D+%5Csqrt%7B2%7D%2B+%5Cfrac%7B35%7D%7B6%7D++%5Csqrt%7B3%7D%7D+)
Espero que te sirva, salu2!!!!
Vamos analizar cada uno para que puedas ver los conceptos
Espero que te sirva, salu2!!!!
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