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Question
Show that:
`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`
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Solution
`"L" . "H" ."S".`
`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`
`=("x"^("a"+"b"))^("a"-"b").("x"^("b"+"c"))^("b"-"c").("x"^("c"+"a"))^("c"-"a")`
`="x"^("a"^2-"b"^2)."x"^("b"^2-"c"^2)."x"^("c"^2-"a"^2)`
`="x"^("a"^2-"b"^2+"b"^2-"c"^2+"c"^2-"a"^2`
`="x"^0`
`=1 ="R"."H"."S".`
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