To simplify this expression, we need to find a common denominator for each fraction.

For the first fraction, u-6/u+6, the common denominator is (u+6)(u-6).

For the second fraction, u+6/u-6, the common denominator is also (u+6)(u-6).

So the expression becomes:

[(u-6)(u-6) + (u+6)(u+6)] / [(u+6)(u-6) - (u-6)(u+6)]

Expanding the numerator, we get:

(u^2 - 12u + 36 + u^2 + 12u + 36) / [(u^2 - 6u + 6u - 36) - (u^2 - 6u + 6u + 36)]

Simplifying further, we get:

(2u^2 + 72) / (-72)

Therefore, the simplified expression is:

-(u^2 + 36) / 36