Question

1divided by1+a tothe power n_m + 1divided by1+a to the power m-n simplify it please​

Answer 1

Answer:-

$\sf \small \frac{1}{1 + {a}^{n - m} } + \frac{1}{1 + {a}^{m - n} }$

$\sf \small = \frac{1}{1 + \frac{ {a}^{n} }{ {a}^{m} } } + \frac{1}{1 + \frac{{a}^{m} }{ {a}^{n} }}$

$\sf \small = \frac{1}{ \frac{ {a}^{m} + {a}^{n} }{ {a}^{m} } } + \frac{1}{\frac{ {a}^{n} + {a}^{m} }{ {a}^{n} }}$

$\sf \small = \frac{ {a}^{m} }{ {a}^{m} + {a}^{n}} + \frac{ {a}^{n} }{ {a}^{n} + {a}^{m}}$

$\sf \small = \frac{ \cancel{{a}^{m} + {a}^{n} }}{ \cancel{ {a}^{m} + {a}^{n}}}$

$\sf = 1$

Hence, the required answer after simplification is 1.