To simplify the expression 4/(√5-√7), we need to rationalize the denominator.

To do this, we multiply the numerator and denominator by the conjugate of the denominator, which is (√5+√7):

4/(√5-√7) * (√5+√7)/(√5+√7)

Expanding the numerator and denominator, we get:

(4√5 + 4√7)/(√5^2 - √7^2)

Simplifying further, we have:

(4√5 + 4√7)/(5 - 7)

(4√5 + 4√7)/(-2)

Now, we can simplify the expression by factoring out a 2 from the numerator:

2(2√5 + 2√7)/(-2)

Canceling out the -2 in the numerator and denominator, we get:

-2√5 - 2√7

Therefore, 4/(√5-√7) simplifies to -2√5 - 2√7.