If abc=1, prove that (1)/(1+a+b⁻¹) + (1)/(1+b+c⁻¹) + (1)/(1+c+a⁻¹) = 1.

9. a) If abc=1, prove that (1)/(1+a+b⁻¹) + (1)/(1+b+c⁻¹) + (1)/(1+c+a⁻¹) = 1. Step 1: Manipulate the terms using the condition abc=1. From abc=1, we can derive: b⁻¹ = ac; c⁻¹ = ab; a⁻¹ = bc Step 2: Substitute these into the given expression. The expression is: (1)/(1+a+b⁻¹) + 11+

Solved: If abc=1, prove that (1)/(1+a+b⁻¹) + (1)/(1+b+c⁻¹)…

9. a) If $abc=1$ , prove that $\frac{1}{1+a+b^{-1}} + \frac{1}{1+b+c^{-1}} + \frac{1}{1+c+a^{-1}} = 1$ .

Step 1: Manipulate the terms using the condition $abc=1$ .
From $abc=1$ , we can derive:
$b^{-1} = ac$
$c^{-1} = ab$
$a^{-1} = bc$

Step 2: Substitute these into the given expression.
The expression is:

If abc=1, prove that (1)/(1+a+b⁻¹) + (1)/(1+b+c⁻¹) + (1)/(1+c+a⁻¹) = 1.

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