Answer:
B. √{x} + √{x - 1}
Step-by-step explanation:
As hinted in the question, we have to simplify the denominator.
To understand it easier, let's imagine we have x - y in the denominator. If we multiply it with x + y we'll get x² - y², right? Check the next line:
(x - y) (x + y) = x² + xy -xy - y² = x² - y²
If we have the square of those nasty square roots, it will be much simpler to deal with. So, let's multiply the initial fraction using x+y, but with the real values:
[tex]\frac{1}{\sqrt{x} - \sqrt{x - 1} } * \frac{\sqrt{x} + \sqrt{x - 1}}{\sqrt{x} - \sqrt{x - 1}} = \frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} }[/tex]
Then we simplify:
[tex]\frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} } = \frac{\sqrt{x} + \sqrt{x - 1}}{(x) - (x - 1) } = \frac{\sqrt{x} + \sqrt{x - 1}}{ 1 }[/tex]
So, the answer is B. √{x} + √{x - 1}
