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If a b c=1, show that 1/(1+a+b^(-1))+1/(...

If `a b c=1,` show that `1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1`

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To show that \[ \frac{1}{1 + a + b^{-1}} + \frac{1}{1 + b + c^{-1}} + \frac{1}{1 + c + a^{-1}} = 1 \] given that \(abc = 1\), follow these steps: ...
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If abc=1, show that (1)/(1+a+b^(-1))+(1)/(1+b+c)+(1)/(1+c+a^(-1))=1

If abc=1, then ((1)/(1+a+b^(-1))+(1)/(1+b+c^(-1))+(1)/(1+c+a^(-1)))=? a.0 b.ab c.1 d.(1)/(ab)

Knowledge Check

  • If a + b + c =3 and none of a, b, and c is equal to 1, then what is the value of (1)/((1 -a ) (1-b))+ (1)/((1 -b ) (1-c)) + (1)/((1 -c) (1-a)) ?

    A
    0
    B
    1
    C
    3
    D
    6

  • If a^(2) = b + c, b^(2) = c + a , c^(2) = a + b then the value of 3 ((1)/( a + 1) +(1)/(b + 1) + (1)/( c + 1)) is

    A
    1
    B
    `(1)/(3)`
    C
    3
    D
    4

  • a ^(2) = b + c, b ^(2) = c + a, c ^(2) = a + b, then the value of 3 ((1)/( a + 1) + (1)/(b + 1) + (1)/( c +1))

    A
    1
    B
    `1/3`
    C
    3
    D
    4

    • Similar Questions

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    If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(b) + (1)/(c)

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    Show that: (1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(b-c)+x^(a-c))=1

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