ABC26GN1968 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2006 · Marks: · Difficulty:
$\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}}=$ ?
(a)0
(b)$\frac{1}{2}$
(c)1
(d)$a^{m+n}$
Answer
Explanation
$\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}}=\frac{1}{\left(1+\frac{a^{n}}{a^{m}}\right)}+\frac{1}{\left(1+\frac{a^{m}}{a^{n}}\right)}$ $$=\frac{a^{m}}{\left(a^{m}+a^{n}\right)}+\frac{a^{n}}{\left(a^{m}+a^{n}\right)}=\frac{\left(a^{m}+a^{n}\right)}{\left(a^{m}+a^{n}\right)}=1 .$$
Explanation as extracted from the printed page; notation may be imperfect.
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