Question

please solve it correctly​

Answer 1

Step-by-step explanation:

$Prove \: that: \frac{1}{1 + {x}^{a - b} } + \frac{1}{1 + {x}^{b - a} } = 1$

We have,

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

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

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

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

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

$⟹1 = 1$

LHS = RHS

Hence, proved: