Respuesta :

You would multiply by 

[tex]\frac{9+\sqrt{14}}{9+\sqrt{14}}[/tex].

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.
calculista

Answer:

[tex]\frac{9+\sqrt{14}}{9+\sqrt{14}}[/tex]

Step-by-step explanation:

we have

[tex]\frac{5-\sqrt{7}}{9-\sqrt{14}}[/tex]

we know that

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

so

[tex]\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}[/tex]

good job