[1] \dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=?

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Aptitude

TNPSC G4

10th CBSE Maths

$\dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=?$

1/2

a^{m + n}

Explanation:

$\dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=\dfrac{1}{\left(1+\dfrac{a^{n}}{a^{m}}\right)}+\dfrac{1}{\left(1+\dfrac{a^{m}}{a^{n}}\right)}$

=$\dfrac{a^{m}}{\left(a^{m}+a^{n}\right)}+\dfrac{a^{n}}{\left(a^{m}+a^{n}\right)}$

=$\dfrac{\left(a^{m}+a^{n}\right)}{\left(a^{m}+a^{n}\right)}$

=1

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