Advertisements
Advertisements
Question
Prove that:
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
Advertisements
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".`
APPEARS IN
RELATED QUESTIONS
Compute:
`1^8xx3^0xx5^3xx2^2`
Compute:
`(27)^(2/3)÷(81/16)^(-1/4)`
Simplify:
`8^(4/3)+25^(3/2)-(1/27)^(-2/3)`
Simplify:
`(2^-3-2^-4)(2^-3+2^-4)`
Evaluate:
`4"x"^0`
Simplify:
`5"z"^16÷15"z"^-11`
Simplify:
`(125"x"^-3)^(1/3)`
Show that:
`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`
Simplify:
`("a"^(2"n"+3)."a"^((2"n"+1)("n"+2)))/(("a"^3)^(2"n"+1)."a"^("n"(2"n"+1)`
Simplify:
`("x"^(2"n"+7).("x"^2)^(3"n"+2))/"x"^(4(2"n"+3)`
