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Question
Prove that:
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
Solution
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
`"L"."H"."S".=1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a")`
`=1/("x"^("a"-"a")+"x"^("a"-"b"))+1/("x"^("b"-"b")+"x"^("b"-"a")`
`=1/("x"^"a"."x"^-"a"+"x"^"a"."x"^-"b")+1/("x"^"b"."x"^-"b"+"x"^"b"."x"^-"a"`
`=1/("x"^"a"("x"^-"a"+"x"^-"b"))+1/("x"^"b"("x"^-"b"+"x"^-"a")`
`=1/(("x"^-"a"+"x"^-"b")) [1/"x"^"a"+1/"x"^"b"]`
`=1/("x"^-"a"+"x"^-"b") ["x"^-"a"+"x"^-"b"]=1="R"."H"."S".`
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