Question

To rationalize the denominator of (5-\sqrt(7))/(9-\sqrt(14)) , you should multiply the expression by which fraction?

Answer 1

You would multiply by 

$\frac{9+\sqrt{14}}{9+\sqrt{14}}$.

When you rationalize the denominator, you multiply by the conjugate of the denominator.  The conjugate is the same numbers and radicals, but with the sign of the radical switched.

Answer 2

Answer:

$\frac{9+\sqrt{14}}{9+\sqrt{14}}$

Step-by-step explanation:

we have

$\frac{5-\sqrt{7}}{9-\sqrt{14}}$

we know that

To rationalize the denominator, multiply by the conjugate of the denominator

so

$\frac{5-\sqrt{7}}{9-\sqrt{14}}*\frac{9+\sqrt{14}}{9+\sqrt{14}}=\frac{(5-\sqrt{7})(9+\sqrt{14})}{9^{2}-14}\\ \\=\frac{(5-\sqrt{7})(9+\sqrt{14})}{67}$