Final answer:
The expression (9n)/(15n²-12n) simplifies to 3 / (5n-4) with the excluded value being n = 4/5 because division by zero is undefined.
Step-by-step explanation:
To simplify the expression (9n)/(15n²-12n), we first factor out the greatest common factor in the denominator, which is 3n. Doing so, we get:
(9n) / (3n(5n-4))
Then, we can cancel out a factor of 3n from the numerator and denominator since they are common factors, leaving us with:
(9n) / (3n(5n-4)) = 3 / (5n-4)
The excluded values are the values of n that would make the denominator equal to zero, since division by zero is undefined. By setting the denominator 5n-4 equal to zero and solving for n, we find that:
5n-4 = 0
n = 4/5
Therefore, the excluded value is n = 4/5.