Add as indicated in the following expression. Write all answers in lowest terms. \( \frac{5}{2(k-2)}+\frac{2}{3(k-2)} \)

To add the two fractions \( \frac{5}{2(k-2)} \) and \( \frac{2}{3(k-2)} \), we first find a common denominator. Since both denominators share the term \( k-2 \), we need to find the least common multiple of the coefficients \( 2 \) and \( 3 \), which is \( 6 \). Now, we can rewrite both fractions with the common denominator: \[ \frac{5}{2(k-2)} = \frac{5 \cdot 3}{2(k-2) \cdot 3} = \frac{15}{6(k-2)} \] \[ \frac{2}{3(k-2)} = \frac{2 \cdot 2}{3(k-2) \cdot 2} = \frac{4}{6(k-2)} \] Now, we can add the fractions together: \[ \frac{15}{6(k-2)} + \frac{4}{6(k-2)} = \frac{15 + 4}{6(k-2)} = \frac{19}{6(k-2)} \] Thus, the final answer, expressed in lowest terms, is: \[ \frac{19}{6(k-2)} \]