Is it always true?

$\frac{x^{a+c}}{x^{a+c}(1+x^{b-c}+x^{b-a})}+\frac{x^{a+b}}{x^{a+b}(1+x^{c-a}+x^{c-b})}+\frac{x^{b+c}}{x^{b+c}(1+x^{a-b}+x^{a-c})}$

$=\frac{x^{a+c}}{x^{a+c}+x^{a+b}+x^{b+c}}+\frac{x^{a+b}}{x^{a+b}+x^{b+c}+x^{a+c}}+\frac{x^{b+c}}{x^{b+c}+x^{a+c}+x^{a+b}}$

$=\frac{x^{a+c}+x^{a+b}+x^{b+c}}{x^{a+c}+x^{a+b}+x^{b+c}}$

$=\boxed{1}$

Let $w = x^{-a} + x^{-b} + x^{-c}$ . The equation now becomes: $\frac{1}{wx^{b}} + \frac{1}{wx^{c}} + \frac{1}{wx^{a}}$ Using exponent rules, we can rewrite this as: $w^{-1}x^{-b} + w^{-1}x^{-c} + w^{-1}x^{-a}$ Notice that we can factor out the $w$ and use substitution. $w^{-1}(x^{-a}+x^{-b}+x^{-c}) = w^{-1}(w) = \frac{w}{w} = \boxed{1}$