Please help
add and simplify if possible
5u/(u^2-16)+u/(u-4)
To add and simplify the expression (5u/(u^2-16)) + (u/(u-4)), we need to find a common denominator and combine the two fractions.
1. Start by factoring the denominators:
The first denominator, u^2-16, can be factored as (u+4)(u-4).
The second denominator, u-4, is already factored.
So, the common denominator is (u+4)(u-4).
2. Rewrite each fraction using the common denominator:
The first fraction, 5u/(u^2-16), can be rewritten as (5u)/((u+4)(u-4)).
The second fraction, u/(u-4), remains the same.
3. Now, the two fractions have a common denominator, so we can add them:
((5u)/((u+4)(u-4))) + (u/(u-4))
4. To add fractions with the same denominator, we simply add the numerators together while keeping the denominator the same:
((5u) + u)/((u+4)(u-4))
5. Combine the numerators:
(5u + u)/((u+4)(u-4)) = 6u/((u+4)(u-4))
Therefore, the simplified expression is 6u/((u+4)(u-4)).