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№2
![( { frac{1}{ {a}^{ sqrt{2} - 1} }) }^{ sqrt{2} + 1} times {a}^{ sqrt{2} + 1} = ( { {a}^{1 - sqrt{2} }) }^{ sqrt{2} + 1 } times {a}^{ sqrt{2} + 1} = {a}^{1 - 2} times {a}^{ sqrt{2} + 1} = {a}^{ - 1 + sqrt{2} + 1 } = {a}^{ sqrt{2} } ( { frac{1}{ {a}^{ sqrt{2} - 1} }) }^{ sqrt{2} + 1} times {a}^{ sqrt{2} + 1} = ( { {a}^{1 - sqrt{2} }) }^{ sqrt{2} + 1 } times {a}^{ sqrt{2} + 1} = {a}^{1 - 2} times {a}^{ sqrt{2} + 1} = {a}^{ - 1 + sqrt{2} + 1 } = {a}^{ sqrt{2} }](https://tex.z-dn.net/?f=%28+%7B+frac%7B1%7D%7B+%7Ba%7D%5E%7B+sqrt%7B2%7D++-+1%7D+%7D%29+%7D%5E%7B+sqrt%7B2%7D++%2B+1%7D++times++%7Ba%7D%5E%7B+sqrt%7B2%7D++%2B+1%7D++%3D+%28+%7B+%7Ba%7D%5E%7B1+-++sqrt%7B2%7D+%7D%29+%7D%5E%7B+sqrt%7B2%7D+%2B+1+%7D++times+%7Ba%7D%5E%7B+sqrt%7B2%7D++%2B+1%7D+%3D++%7Ba%7D%5E%7B1+-+2%7D++times++%7Ba%7D%5E%7B+sqrt%7B2%7D++%2B+1%7D++%3D++%7Ba%7D%5E%7B+-+1+%2B++sqrt%7B2%7D+%2B+1+%7D++%3D++%7Ba%7D%5E%7B+sqrt%7B2%7D+%7D+)
№5
![frac{ sqrt{ {a}^{3} } - a}{a - 2 {a}^{ frac{1}{2} } + 1 } = frac{a( {a}^{ frac{1}{2} } - 1) }{( { {a}^{ frac{1}{2} } - 1 })^{2} } = frac{a}{{a}^{ frac{1}{2} } - 1 } frac{ sqrt{ {a}^{3} } - a}{a - 2 {a}^{ frac{1}{2} } + 1 } = frac{a( {a}^{ frac{1}{2} } - 1) }{( { {a}^{ frac{1}{2} } - 1 })^{2} } = frac{a}{{a}^{ frac{1}{2} } - 1 }](https://tex.z-dn.net/?f=+frac%7B+sqrt%7B+%7Ba%7D%5E%7B3%7D+%7D++-+a%7D%7Ba+-+2+%7Ba%7D%5E%7B+frac%7B1%7D%7B2%7D+%7D+%2B+1+%7D++%3D++frac%7Ba%28+%7Ba%7D%5E%7B+frac%7B1%7D%7B2%7D+%7D+-+1%29+%7D%7B%28+%7B+%7Ba%7D%5E%7B+frac%7B1%7D%7B2%7D+%7D+-+1+%7D%29%5E%7B2%7D+%7D++%3D++frac%7Ba%7D%7B%7Ba%7D%5E%7B+frac%7B1%7D%7B2%7D+%7D+-+1+%7D+)
№5
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