Final answer:
To add fractions with different denominators, we first find the least common multiple as the common denominator. Then, we rewrite the fractions to have the common denominator and add them together. The restriction in this case is that n cannot be equal to 4 or 6/5.
Step-by-step explanation:
To add the fractions \(\frac{3}{n-4}\) and \(\frac{3}{5n-6}\), we need to find a common denominator. The least common multiple (LCM) of \((n-4)\) and \((5n-6)\) is \((n-4)(5n-6)\). Now we can rewrite the fractions with the common denominator:
\(\frac{3}{n-4} = \frac{3(5n-6)}{(n-4)(5n-6)}\) and \(\frac{3}{5n-6} = \frac{3(n-4)}{(n-4)(5n-6)}\)
Adding the fractions together, we get:
\(\frac{3(5n-6) + 3(n-4)}{(n-4)(5n-6)} = \frac{15n-18 + 3n-12}{(n-4)(5n-6)} = \frac{18n-30}{(n-4)(5n-6)}\)
The restriction in this case is that \(n\) cannot be equal to either 4 or \(\frac{6}{5}\). Since these values would result in a zero denominator, which is undefined.