Simplify. Express your answer as a single fraction in simplest form \( \frac{7}{18 t+6}-\frac{7}{9 t+3} \)

To simplify the expression \( \frac{7}{18t+6} - \frac{7}{9t+3} \), we first notice that \(18t + 6\) can be factored as \(6(3t + 1)\) and \(9t + 3\) can be factored as \(3(3t + 1)\). Therefore, we rewrite the fractions: \[ \frac{7}{6(3t + 1)} - \frac{7}{3(3t + 1)} \] Next, we need a common denominator, which is \(6(3t + 1)\). We can rewrite the second fraction with this common denominator: \[ \frac{7}{6(3t + 1)} - \frac{7 \cdot 2}{6(3t + 1)} = \frac{7}{6(3t + 1)} - \frac{14}{6(3t + 1)} \] Now, we can combine the fractions: \[ \frac{7 - 14}{6(3t + 1)} = \frac{-7}{6(3t + 1)} \] Thus, the simplified expression is: \[ \frac{-7}{6(3t + 1)} \] This is the final answer expressed as a single fraction in simplest form.