Question

Exponents and powers

Evaluate the above sum​

Answer 1

Step-by-step explanation:

We have,

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

$= \frac{1}{1 + \dfrac{{x}^{a }}{ {x}^{b} } } + \frac{1}{1 + \dfrac{{x}^{b } }{ {x}^{a} }}$

$= \frac{1}{ \dfrac{ {x}^{b} + {x}^{a }}{ {x}^{b} } } + \frac{1}{ \dfrac{ {x}^{a} + {x}^{b } }{ {x}^{a} }}$

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

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

$= 1$