Question$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1$

Studdy Solution
Rearrange and solve the equation:
$3 = 1 + a + \frac{1}{a}$ $2 = a + \frac{1}{a}$
Multiply through by $a$ to clear the fraction:
$2a = a^2 + 1$
Rearrange into a standard quadratic form:
$a^2 - 2a + 1 = 0$
Factor the quadratic:
$(a - 1)^2 = 0$
Solve for $a$:
$a = 1$
Since we assumed $a = b = c$, we have $a = b = c = 1$.
The solution is $a = 1, b = 1, c = 1$.