Question

\[ \frac{1}{1+x^{a-b}} + \frac{1}{1+x^{b-a}} \]

Solution

\[ = \frac{1}{1+\frac{x^a}{x^b}} + \frac{1}{1+\frac{x^b}{x^a}} \] \[ = \frac{1}{\frac{x^b + x^a}{x^b}} + \frac{1}{\frac{x^a + x^b}{x^a}} \] \[ = \frac{x^b}{x^a + x^b} + \frac{x^a}{x^a + x^b} \] \[ = \frac{x^b + x^a}{x^a + x^b} \] \[ = 1 \]

Answer

\[ \boxed{1} \]

Next Question / Full Exercise