problem is attached, i got as far as (√x)(√(x+1)-√(x-1)).
$\displaystyle {\sqrt{x^2+x} - \sqrt{x^2-x}} \cdot \frac{\sqrt{x^2+x} + \sqrt{x^2-x}}{\sqrt{x^2+x} + \sqrt{x^2-x}} =$
$\displaystyle \frac{(x^2+x) - (x^2-x)}{\sqrt{x^2+x} + \sqrt{x^2-x}}=$
$\displaystyle \frac{2x}{\sqrt{x^2+x} + \sqrt{x^2-x}} =$
divide numerator by $\displaystyle x$ , denominator by $\displaystyle \sqrt{x^2}$ ... ( note: since $\displaystyle x > 0$ , $\displaystyle x = \sqrt{x^2}$ )
$\displaystyle \frac{2}{\sqrt{1+\frac{1}{x}} + \sqrt{1- \frac{1}{x}}}$
now take the limit as $\displaystyle x \to \infty$