Question

Prove that :

The question is attached above

It will be really very helpful if you solve this in a rough notebook and share the picture of it​

Answer 1

Answer:

Refer to the image.

The image given above is the answer.

Step-by-step explanation:

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Answer 2

$\underline{\large \sf{Given-} }$

$\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ \leadsto\displaystyle{\dfrac{1}{1 + x^{a - b}}{1}{1 + x^{b - a}} =1}}$

$\underline{\large \sf{To \: Prove-} }$

1 = 1

$\underline{\large \sf{Solution-} }$

Consider L.H.S->

$\sf \implies{\dfrac{1}{1 + x^{a - b}} + \dfrac{1}{1 + x^{b - a}}}$

$\sf \implies{\dfrac{1}{1 + \dfrac{x^a}{x^b}} + \dfrac{1}{1 + \dfrac{x^b}{x^a}}}$

$\sf \implies{\dfrac{1}{\dfrac{x^b + x^a}{x^b}} + \dfrac{1}{\dfrac{x^a + x^b}{x^a}}}$

$\sf \implies \dfrac{x^b}{x^b + x^a} + \dfrac{x^a}{x^a + x^b}$

$\ \ \ \ \ \ \ \ \ \ \ \ \dashrightarrow{\underbrace{\boxed{\bf\color{blue}{\dfrac {\cancel{x^b + x^a}}{\cancel{x^a + x^b}} \: \color{pink}{=} \: \: \: \color{magenta}{1}}}}}$

1 = 1

L.H.S = R.H.S

Hence Proved✓