Answer:
To rationalize the denominator of 5/√3+√7, we can multiply the numerator and denominator by the conjugate of the denominator, which is √3-√7.
The product of (√3+√7) and (√3-√7) is the difference of squares, which is (√3)^2 - (√7)^2 = 3-7 = -4.
Thus, we have:
5/√3+√7 * (√3-√7)/(√3-√7) = 5(√3-√7)/(-4) = -5/4(√7-√3)
Therefore, the rationalizing factor is (√3-√7).