1.

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

Answer»

wer:-

\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.


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