Maths Question:
Simplify as much as possible $\frac{1}{x-\sqrt{{{x}^{2}}-1}}$
Maths Solution:
$\begin{align} & \frac{1}{x-\sqrt{{{x}^{2}}-1}}=\frac{1}{x-\sqrt{{{x}^{2}}-1}}\times \frac{x+\sqrt{{{x}^{2}}-1}}{x+\sqrt{{{x}^{2}}-1}}=\frac{x+\sqrt{{{x}^{2}}-1}}{{{x}^{2}}-({{x}^{2}}-1)} \\ & \frac{1}{x-\sqrt{{{x}^{2}}-1}}=\frac{x+\sqrt{{{x}^{2}}-1}}{{{x}^{2}}-{{x}^{2}}+1}=x+\sqrt{{{x}^{2}}-1} \\\end{align}$
University mathstopic: