To rationalize the denominator of the fraction with numerator 5 minus square root of 7 and denominator 9 minus square root of 14 , you should multiply the expression by which fraction?

To remove the radical from the denominator, multiply by the conjugate of 9 − √14, which is 9 + √14, over itself. The denominator then becomes (9 − √14)(9 + √14) = 9² − (√14)² = 81 − 14 = 67, a rational number. So the correct choice is the fraction with numerator and denominator both equal to 9 + √14.

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