Question

p-√p^2+1 ÷ p^2-(p^2+1) = -p + √p^2+1 . prove.

Answer 1

$\textbf{- Proof -}$

$Now, \: \: L.H.S. \\ \\ = \frac{p - \sqrt{ {p}^{2} + 1} }{ {p}^{2} - ( {p}^{2} + 1)} \\ \\ = \frac{p - \sqrt{ {p}^{2} + 1} }{ {p}^{2} - {p}^{2} - 1} \\ \\ = \frac{p - \sqrt{ {p}^{2} + 1 } }{- 1} \\ \\ = - p + \sqrt{ {p}^{2} + 1} \\ \\ = R.H.S. \: \: (Proved)$

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