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
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