If `a, b, c` are positive real numbers such that `a + b + c = 1`, then prove that `a/(b + c)+b/(c+a) + c/(a+b) >= 3/2`

Explanation

To prove that \( \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} \geq \frac{3}{2} \) given that \( a + b + c = 1 \) and \( a, b, c > 0 \), we can follow these steps:

### Step 1: Rewrite the Denominators
Since \( a + b + c = 1 \), we can express the denominators in terms of \( a, b, c \):
- \( b + c = 1 - a \)
- \( c + a = 1 - b \)
- \( a + b = 1 - c \)

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