Answer
Fill the blank with
$(\sqrt{x+7}+\sqrt{x})$
Work Step by Step
The numerator is rationalized by applying the difference of squares formula,
$(a-b)(a+b)=a^{2}-b^{2}$
Multiplying with the conjugate of the numerator, $\sqrt{x+7}+\sqrt{x}$, the numerator becomes
$(x+7)-x=7\qquad $... no radicals.
and the denominator becomes $7(\sqrt{x+7}+\sqrt{x})$.
Fill the blank with
$(\sqrt{x+7}+\sqrt{x})$
