Question

prove that (1/1+x^m-n) + (1/1+x^n-m)=1​

Answer 1

Step-by-step explanation:

$\frac{1}{1 + {x}^{m - n} } + \frac{1}{ 1 + {x}^{n - m} }$

$\frac{1}{1 + {x}^{m - n} } + \frac{1}{ 1 + {x}^{ - (m - n)} }$

$\frac{1}{1 + {x}^{m - n} } + \frac{1}{ 1 + \frac{1}{ {x}^{m - n} } }$

$\frac{1}{1 + {x}^{m - n} } + \frac{ {x}^{m - n} }{ {x}^{m - n} + 1 }$

$\frac{ 1 + {x}^{m - n} }{1 + {x}^{m - n} }$

1