1. **State the problem:** Solve the equation $$\frac{9t+27}{9t+18} = 9$$ for $t$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides by the denominator to eliminate the fraction, then solve the resulting linear equation. 3. **Multiply both sides by the denominator:** $$9t + 27 = 9(9t + 18)$$ 4. **Expand the right side:** $$9t + 27 = 81t + 162$$ 5. **Bring all terms involving $t$ to one side and constants to the other:** $$9t - 81t = 162 - 27$$ 6. **Simplify both sides:** $$-72t = 135$$ 7. **Divide both sides by $-72$ to solve for $t$:** $$t = \frac{135}{-72} = -\frac{135}{72}$$ 8. **Simplify the fraction by dividing numerator and denominator by 9:** $$t = -\frac{15}{8}$$ **Final answer:** $$t = -\frac{15}{8}$$