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, but be careful to check for values that make the denominator zero. 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 to one side to isolate $t$:** $$9t + 27 - 81t - 162 = 0$$ 6. **Simplify:** $$-72t - 135 = 0$$ 7. **Solve for $t$:** $$-72t = 135$$ $$t = \frac{135}{-72} = -\frac{15}{8}$$ 8. **Check for restrictions:** The denominator $9t + 18$ cannot be zero. Set denominator to zero: $$9t + 18 = 0 \implies t = -2$$ Since $t = -\frac{15}{8} \neq -2$, the solution is valid. **Final answer:** $$t = -\frac{15}{8}$$