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1)
![frac{c}{9-c} : frac{c^{ frac{3}{2} }}{3c^{ frac{1}{2} }-c}= frac{c}{(3-c^{ frac{1}{2} })(3+c^{ frac{1}{2} })}* frac{c^{ frac{1}{2} }(3-c^{ frac{1}{2} })}{c^{ frac{1}{2} }*c}= frac{1}{3+c^{ frac{1}{2} }} frac{c}{9-c} : frac{c^{ frac{3}{2} }}{3c^{ frac{1}{2} }-c}= frac{c}{(3-c^{ frac{1}{2} })(3+c^{ frac{1}{2} })}* frac{c^{ frac{1}{2} }(3-c^{ frac{1}{2} })}{c^{ frac{1}{2} }*c}= frac{1}{3+c^{ frac{1}{2} }}](https://tex.z-dn.net/?f=+frac%7Bc%7D%7B9-c%7D+%3A+frac%7Bc%5E%7B+frac%7B3%7D%7B2%7D+%7D%7D%7B3c%5E%7B+frac%7B1%7D%7B2%7D+%7D-c%7D%3D+frac%7Bc%7D%7B%283-c%5E%7B+frac%7B1%7D%7B2%7D+%7D%29%283%2Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%29%7D%2A+frac%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%283-c%5E%7B+frac%7B1%7D%7B2%7D+%7D%29%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%2Ac%7D%3D+frac%7B1%7D%7B3%2Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D+)
2)
![frac{3}{c+3c^{ frac{1}{2} }}+ frac{1}{3+c^{ frac{1}{2} }}= frac{3}{c^{ frac{1}{2} }(c^{ frac{1}{2} }+3)}+ frac{1}{c^{ frac{1}{2} }+3}= frac{3+c^{ frac{1}{2} }}{c^{ frac{1}{2} }(c^{ frac{1}{2} }+3)}= frac{1}{c^{ frac{1}{2} }} frac{3}{c+3c^{ frac{1}{2} }}+ frac{1}{3+c^{ frac{1}{2} }}= frac{3}{c^{ frac{1}{2} }(c^{ frac{1}{2} }+3)}+ frac{1}{c^{ frac{1}{2} }+3}= frac{3+c^{ frac{1}{2} }}{c^{ frac{1}{2} }(c^{ frac{1}{2} }+3)}= frac{1}{c^{ frac{1}{2} }}](https://tex.z-dn.net/?f=+frac%7B3%7D%7Bc%2B3c%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D%2B+frac%7B1%7D%7B3%2Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D%3D+frac%7B3%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%28c%5E%7B+frac%7B1%7D%7B2%7D+%7D%2B3%29%7D%2B+frac%7B1%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%2B3%7D%3D+frac%7B3%2Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%28c%5E%7B+frac%7B1%7D%7B2%7D+%7D%2B3%29%7D%3D+frac%7B1%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D++++++)
3)
![( frac{1}{c^{ frac{1}{2} }} )^{-2}=(c^{ frac{1}{2} })^2=c ( frac{1}{c^{ frac{1}{2} }} )^{-2}=(c^{ frac{1}{2} })^2=c](https://tex.z-dn.net/?f=%28+frac%7B1%7D%7Bc%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D+%29%5E%7B-2%7D%3D%28c%5E%7B+frac%7B1%7D%7B2%7D+%7D%29%5E2%3Dc)
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