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Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=...

Prove that: `1/(1+x^(a-b))+1/(1+x^(b-a))=1`

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AI Generated Solution

To prove that: \[ \frac{1}{1 + x^{a-b}} + \frac{1}{1 + x^{b-a}} = 1 \] Let's follow these steps: ### Step 1: Rewrite the expression using a common base First, note that \( x^{a-b} \) and \( x^{b-a} \) are reciprocals of each other. This is because: \[ x^{b-a} = \frac{1}{x^{a-b}} \] ...
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Show that: (1)/(1+x^(a-b))+(1)/(1+x^(b-a))=1

Prove 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

Knowledge Check

  • Find the value of (1)/(1+x^(a-b))+(1)/(1+x^(b-a))

    A
    0
    B
    `-1`
    C
    1
    D
    `x^(a+b)`

  • Find the value of (1)/(1+x^(a-b))+(1)/(1+x^(b-a))

    A
    0
    B
    -1
    C
    1
    D
    `x^(a+b)`

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