We have, #10; #10; √(1+e^x1 e^x) #10; #10; =√(1+e^x1 e^x×1 e^x1 e^x) #10; #10; #10; =√(1+e^x1 e^x×1 e^x1 e^x) On rationlize ...

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Finding Square Root through Prime Factorisation

Solve : √1+...

Question

Solve : $\sqrt{\frac{1 + e^{x}}{1 - e^{x}}}$

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Solution

We have,

$\sqrt{\frac{1 + e^{x}}{1 - e^{x}}}$

$= \sqrt{\frac{1 + e^{x}}{1 - e^{x}} \times \frac{1 - e^{x}}{1 - e^{x}}}$

$= \sqrt{\frac{1 + e^{x}}{1 - e^{x}} \times \frac{1 - e^{x}}{1 - e^{x}}} O n r a t i o n l i z e$

$= \sqrt{\frac{1^{2} - e^{2 x}}{{(1 - e^{x})}^{2}}}$

$= \frac{\sqrt{1 - e^{2 x}}}{(1 - e^{x})}$
Hence, this is the answer.

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