Question

show that 1÷1+x power a-b+1÷1+x power b-a =1​

Answer 1

Step-by-step explanation:

We have to prove that,

\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}=1

L.H.S.

\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}

=\frac{1}{1+\frac{x^a}{x^b}}+\frac{1}{1+\frac{x^b}{x^a}}

( Since, a^{m-n}=\frac{a^m}{a^n} )

=\frac{1}{\frac{x^b+x^a}{x^a}}+\frac{1}{\frac{x^a+x^b}{x^a}}

=\frac{x^a}{x^b+x^a}+\frac{x^a}{x^a+x^b}

=\frac{x^a+x^b}{x^a+x^b}

=1

= R.H.S.

Hence, proved.

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Answer 2

Answer:

The given equation is:

\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}

=\frac{1}{1+\frac{x^a}{x^b}}+\frac{1}{1+\frac{x^b}{x^a}}

=\frac{1}{\frac{x^b+x^a}{x^b}}+\frac{1}{\frac{x^a+x^b}{x^a}}

=\frac{x^b}{x^b+x^a}+\frac{x^a}{x^b+x^a}

=\frac{x^a+x^b}{x^a+x^b}

=1

Thus, the value of the given equation is 1.

Step-by-step explanation:

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