Ответ:
[tex] \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{ {c}^{ \frac{3}{2} } - {d}^{ \frac{3}{2} } } = \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{({c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } ) \left( ({c}^{ \frac{1}{2} } )^{2} + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + ( {d}^{ \frac{1}{2} } )^{2} \right) } = \\ = \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{({c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } ) \left( c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d \right) } = \frac{1}{ {c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } } = \frac{1}{ \sqrt{c} - \sqrt{d} } [/tex]
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Answers & Comments
Ответ:
[tex] \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{ {c}^{ \frac{3}{2} } - {d}^{ \frac{3}{2} } } = \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{({c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } ) \left( ({c}^{ \frac{1}{2} } )^{2} + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + ( {d}^{ \frac{1}{2} } )^{2} \right) } = \\ = \frac{c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d}{({c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } ) \left( c + {c}^{ \frac{1}{2} } {d}^{ \frac{1}{2} } + d \right) } = \frac{1}{ {c}^{ \frac{1}{2} } - {d}^{ \frac{1}{2} } } = \frac{1}{ \sqrt{c} - \sqrt{d} } [/tex]