The answer is:  " √3 " .
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      →  The simplified expression is:  " √3 " .
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Step-by-step explanation:
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We are given:
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 →    ;
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Note the "imaginary number" —  " √(-1) " —
        which is represented by the symbol:  " *i* "  .
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So, let us factor out Both the numerator And the denominator:
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Start with the "numerator" ; as follows:
The numerator is:  √(-30) ;  which factors into:
           Â
               →  √-1 * √30 ;
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Note that:  " √-1 " ; is an imaginary number; which is represented
               by the symbol:  " *i* "  .
As such, we can rewrite the numerator as:
               →  *i* √30  .
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The denominator is:  √(-10) ; which factors into:
               →  √-1  * √10  ;
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As noted above:
      →   " √-1 "  ;  is an imaginary number; which is represented
                  by the symbol:  " *i* "  .
As such, we can rewrite the denominator as:
               →  *i* √10  .
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Now, let us rewrite the entire expression:
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     ( *i* √30)
    ____________
     ( *i* √10)  Â
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Note:  The  *i*  symbols "cancel out" to:  " 1 " ; Â
Â
  →  { since:  any "non-zero value" ;  divided by "that same value" ;
          is equal to:  "1 " .} ;
  →  { i.e.,  in our case:  [ *i*  ÷  *i* ] ;  that is;  " [*i* / *i* ], equals : " 1 " .}.
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And we are left with:
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  →  " " .
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Note that both the numerator and the denominator are "square roots" —  Â
      and furthermore — are square roots of a "positive number".
Specifically, the "numerator" is:  " √30 " ;
    And  the "denominator is:  " √10 " .
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 →   Note that the numerator:  " √30 " ;
        →   can be factored into:  "√10 * √3 " ;
 →   And that the "denominator" ;  which is:  " √10 " ;  is one of the aforementioned 'factors' of the "numerator" .
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Let us rewrite the expression — and further simplify:
     →    ;
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  =   ;
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Note:  The "(√10)" values,  "cancel out"  to:  "1" ;
   Â
→  {since:  any "non-zero value" ;  divided by "that same value" ;
          is equal to:  "1 " .} ;
                    Â
     →  { i.e.,  in our case:  [" √10 ÷ √10 " ] ; Â
     →  that is;  [ " " ]" ;
                    →  equals : " 1 " .}.
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→  and we are left with:  " (√3) / 1 " ;
      →  which equals:  " √3  "  ; Â
      →  which is our answer.
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Hope this is helpful to you.
   Best wishes in your academic endeavors
       — and within the "" community!
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