To rationalize the denominator of 5-√7/9-√14, you should multiply the expression by which fractions?

5+√7
9-√14

9-√14
9-√14

9+√14
9+√14

√14
√14

Answer

9+√14

Explanation

To Rationalize the denominator of 5-√7/9-√14.

To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

                        =  (5-√7)(9+√14)/(9²-14)

                       = (45 + 5√14 - 9√7 - √98)/(81-14)

                        =  (45 + 5√14 - 9√7 - √98)/67

                        = (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.  

The denominator is (9-√14) and its conjugate is (9+√14).

56

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