Respuesta :
You can use the rationalization method in which we multiply the fraction with conjugate of the denominator.
The expression needed to rationalize the denominator of fraction is
[tex]9 + \sqrt{14}[/tex]
How to rationalize a fraction ?
Suppose the given fraction is [tex]\dfrac{a}{b + c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} = \dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}\\\\\\(since \: \: (x+y)(x-y) = x^2 - y^2 )[/tex]
We actually rationalize just for the use of that later denominator or numerator(if they seem to be helpful).
Remember that [tex]\dfrac{b-c}{b-c} = 1[/tex] thus, multiplying it with the fraction doesn't change its value, and just change the way how it looks. We assume that b-c is not 0
Using above method for getting the expression needed
Since the given fraction is
[tex]\dfrac{5 - \sqrt{7}}{9 - \sqrt{14}}[/tex]
Thus, the conjugate denominator would be [tex]9 + \sqrt{14}[/tex]
Thus,
The expression needed to rationalize the denominator of fraction is
[tex]9 + \sqrt{14}[/tex]
Learn more about rationalizing fractions here:
https://brainly.com/question/14261303
