Answer
$\displaystyle \frac{x+3\sqrt{x}-10}{x-25}$
Work Step by Step
We lose the square roots in the denominator by applying the difference of squares formula:
$(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$
$\displaystyle \frac{\sqrt{x}-2}{\sqrt{x}-5}\color{red}{ \cdot\frac{\sqrt{x}+5}{\sqrt{x}+5} }\qquad$ (rationalize)
$=\displaystyle \frac{(\sqrt{x}-2)(\sqrt{x}+5)}{(\sqrt{x})^{2}-(5)^{2}}$
... use FOIL for the numerator
$=\displaystyle \frac{(\sqrt{x})^{2}+5\sqrt{x}-2\sqrt{x}-10}{x-25}$
$=\displaystyle \frac{x+3\sqrt{x}-10}{x-25}$
