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535.
![frac{a}{3 sqrt{5} } = frac{a sqrt{5} }{3 sqrt{5} sqrt{5} } = frac{a sqrt{5} }{3( sqrt{5})^2} = frac{a sqrt{5} }{3*5} = frac{a sqrt{5} }{15} \ \
frac{4b}{5 sqrt{c} } = frac{4b* sqrt{c} }{5*( sqrt{c} )^2} = frac{4b sqrt{c} }{5c} \ \
frac{6}{ sqrt{a+b}} = frac{6 sqrt{a+b} }{( sqrt{a+b} )^2} = frac{6 sqrt{a+b} }{a+b} \ \
frac{4}{ sqrt{x-y} } = frac{4 sqrt{x-y} }{x-y} \ \](https://tex.z-dn.net/?f=+frac%7Ba%7D%7B3+sqrt%7B5%7D+%7D+%3D++frac%7Ba+sqrt%7B5%7D+%7D%7B3+sqrt%7B5%7D+sqrt%7B5%7D++%7D+%3D++frac%7Ba+sqrt%7B5%7D+%7D%7B3%28+sqrt%7B5%7D%29%5E2%7D+%3D++frac%7Ba+sqrt%7B5%7D+%7D%7B3%2A5%7D+%3D+frac%7Ba+sqrt%7B5%7D+%7D%7B15%7D++%5C++%5C+%0A+frac%7B4b%7D%7B5+sqrt%7Bc%7D+%7D+%3D+++frac%7B4b%2A+sqrt%7Bc%7D+%7D%7B5%2A%28+sqrt%7Bc%7D+%29%5E2%7D+%3D++frac%7B4b+sqrt%7Bc%7D+%7D%7B5c%7D++%5C++%5C+%0A+frac%7B6%7D%7B+sqrt%7Ba%2Bb%7D%7D+%3D++frac%7B6+sqrt%7Ba%2Bb%7D+%7D%7B%28+sqrt%7Ba%2Bb%7D+%29%5E2%7D+%3D++frac%7B6+sqrt%7Ba%2Bb%7D+%7D%7Ba%2Bb%7D++%5C++%5C+%0A+frac%7B4%7D%7B+sqrt%7Bx-y%7D+%7D+%3D++frac%7B4+sqrt%7Bx-y%7D+%7D%7Bx-y%7D++%5C++%5C+%0A "frac{a}{3 sqrt{5} } = frac{a sqrt{5} }{3 sqrt{5} sqrt{5} } = frac{a sqrt{5} }{3( sqrt{5})^2} = frac{a sqrt{5} }{3*5} = frac{a sqrt{5} }{15} \ \
frac{4b}{5 sqrt{c} } = frac{4b* sqrt{c} }{5*( sqrt{c} )^2} = frac{4b sqrt{c} }{5c} \ \
frac{6}{ sqrt{a+b}} = frac{6 sqrt{a+b} }{( sqrt{a+b} )^2} = frac{6 sqrt{a+b} }{a+b} \ \
frac{4}{ sqrt{x-y} } = frac{4 sqrt{x-y} }{x-y} \ \")
![frac{16}{ sqrt{a} + sqrt{6} } = frac{16( sqrt{a}- sqrt{6} ) }{( sqrt{a}+ sqrt{6})( sqrt{a} - sqrt{6}) } = frac{16 sqrt{a}- 16sqrt{6} }{( sqrt{a} )^2- ( sqrt{6})^2 } = frac{16 sqrt{a} -16 sqrt{6} }{a-6} \ \
frac{a}{ sqrt{c}-4} = frac{a (sqrt{c}+4) }{( sqrt{c}-4)( sqrt{c} +4) } = frac{a sqrt{c}+4a }{c-16}](https://tex.z-dn.net/?f=+frac%7B16%7D%7B+sqrt%7Ba%7D+%2B+sqrt%7B6%7D+%7D+%3D++frac%7B16%28+sqrt%7Ba%7D-+sqrt%7B6%7D+%29+%7D%7B%28+sqrt%7Ba%7D%2B+sqrt%7B6%7D%29%28+sqrt%7Ba%7D+-+sqrt%7B6%7D%29++++%7D+%3D++frac%7B16+sqrt%7Ba%7D-+16sqrt%7B6%7D++%7D%7B%28+sqrt%7Ba%7D+%29%5E2-+%28+sqrt%7B6%7D%29%5E2+%7D+%3D++frac%7B16+sqrt%7Ba%7D+-16+sqrt%7B6%7D+%7D%7Ba-6%7D++%5C++%5C+%0A+frac%7Ba%7D%7B+sqrt%7Bc%7D-4%7D+%3D++frac%7Ba+%28sqrt%7Bc%7D%2B4%29++%7D%7B%28+sqrt%7Bc%7D-4%29%28+sqrt%7Bc%7D+%2B4%29++%7D+%3D++frac%7Ba+sqrt%7Bc%7D%2B4a+%7D%7Bc-16%7D+ "frac{16}{ sqrt{a} + sqrt{6} } = frac{16( sqrt{a}- sqrt{6} ) }{( sqrt{a}+ sqrt{6})( sqrt{a} - sqrt{6}) } = frac{16 sqrt{a}- 16sqrt{6} }{( sqrt{a} )^2- ( sqrt{6})^2 } = frac{16 sqrt{a} -16 sqrt{6} }{a-6} \ \
frac{a}{ sqrt{c}-4} = frac{a (sqrt{c}+4) }{( sqrt{c}-4)( sqrt{c} +4) } = frac{a sqrt{c}+4a }{c-16}")
536.
![frac{16}{ sqrt{2}+ sqrt{3} +1 } = frac{16( sqrt{2}- sqrt{3} -1) }{( sqrt{2}+ sqrt{3}+1)( sqrt{2} - sqrt{3} -1) } = \ \
= frac{16 sqrt{2} -16 sqrt{3}-16 }{2- sqrt{6}- sqrt{2}+ sqrt{6} -3- sqrt{3} + sqrt{2}- sqrt{3}-1 } = frac{-2(8 sqrt{2}+8 sqrt{3}+8) }{-2} = \ \
=8( sqrt{2} + sqrt{3} +1)](https://tex.z-dn.net/?f=+frac%7B16%7D%7B+sqrt%7B2%7D%2B+sqrt%7B3%7D+%2B1+%7D+%3D++frac%7B16%28+sqrt%7B2%7D-+sqrt%7B3%7D+-1%29+%7D%7B%28+sqrt%7B2%7D%2B+sqrt%7B3%7D%2B1%29%28+sqrt%7B2%7D+-+sqrt%7B3%7D+-1%29+%7D+%3D+%5C++%5C+%0A%3D++frac%7B16+sqrt%7B2%7D+-16+sqrt%7B3%7D-16+%7D%7B2-+sqrt%7B6%7D-+sqrt%7B2%7D%2B+sqrt%7B6%7D+-3-+sqrt%7B3%7D+%2B+sqrt%7B2%7D-+sqrt%7B3%7D-1++%7D+%3D++frac%7B-2%288+sqrt%7B2%7D%2B8+sqrt%7B3%7D%2B8%29++%7D%7B-2%7D+%3D+%5C++%5C+%0A%3D8%28+sqrt%7B2%7D+%2B+sqrt%7B3%7D+%2B1%29 "frac{16}{ sqrt{2}+ sqrt{3} +1 } = frac{16( sqrt{2}- sqrt{3} -1) }{( sqrt{2}+ sqrt{3}+1)( sqrt{2} - sqrt{3} -1) } = \ \
= frac{16 sqrt{2} -16 sqrt{3}-16 }{2- sqrt{6}- sqrt{2}+ sqrt{6} -3- sqrt{3} + sqrt{2}- sqrt{3}-1 } = frac{-2(8 sqrt{2}+8 sqrt{3}+8) }{-2} = \ \
=8( sqrt{2} + sqrt{3} +1)")
536.
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