Sqrt[z/(1 + z)] == Sqrt[z]/Sqrt[1 + z]

Cell[BoxData[RowBox[List[SqrtBox[FractionBox["z", RowBox[List["1", "+", "z"]]]], "\[Equal]", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msqrt> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> &#10869; </mo> <mfrac> <msqrt> <mi> z </mi> </msqrt> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[FractionBox["z_", RowBox[List["1", "+", "z_"]]]], "]"]], "\[RuleDelayed]", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]

2001-10-29