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Maths-

General

Easy

Question

Find the value of [1 / (1 + x^−𝑚 )] + [1 / (1+x^𝑚)]

hint Hint:

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a n times.

The correct answer is: Simplifying the given expression, we get 1.

Step-by-step solution:-
[1 / (1 + x^−m)] + [1 / (1+x^m)]
= [1 / (1 + 1/x^m)] + [1 / (1+x^m)] …..................................... [b^-n = 1/bⁿ]
= [1 / (x^m / x^m + 1 / x^m] + [1 / (1+x^m)]
= [1 / (x^m + 1 / x^m] + [1 / (1+x^m)]
= [x^m / (x^m + 1)] + [1 / (1+x^m)]
= (x^m + 1) / (x^m + 1)
= 1.
Final Answer:-
∴ Simplifying the given expression, we get 1.

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