Sqrt[Subscript[z, 1]/Subscript[z, 2]] == (1/Sqrt[Subscript[z, 2]/(Subscript[z, 2] - Subscript[z, 1])]) Sqrt[Subscript[z, 1]/(Subscript[z, 2] - Subscript[z, 1])] /; Element[Subscript[z, 2] - Subscript[z, 1], Reals] && Subscript[z, 2] != Subscript[z, 1]

Cell[BoxData[RowBox[List[RowBox[List[SqrtBox[FractionBox[SubscriptBox["z", "1"], RowBox[List[" ", SubscriptBox["z", "2"]]]]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox[FractionBox[SubscriptBox["z", "2"], RowBox[List[SubscriptBox["z", "2"], "-", SubscriptBox["z", "1"]]]]]], SqrtBox[FractionBox[SubscriptBox["z", "1"], RowBox[List[SubscriptBox["z", "2"], "-", SubscriptBox["z", "1"]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["z", "2"], "-", SubscriptBox["z", "1"]]], "\[Element]", "Reals"]], "\[And]", RowBox[List[SubscriptBox["z", "2"], "\[NotEqual]", SubscriptBox["z", "1"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msqrt> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> </msqrt> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mfrac> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> </msqrt> </mfrac> <mo> &#8290; </mo> <msqrt> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8800; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <reals /> </apply> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SqrtBox[FractionBox[SubscriptBox["zz", "1"], RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]]]], SqrtBox[FractionBox[SubscriptBox["zz", "2"], RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["zz", "2"], "\[NotEqual]", SubscriptBox["zz", "1"]]]]]]]]]]]

2001-10-29