1. The problem is to simplify the expression $\frac{54y + 2y^2 - 15y + 10}{9 + 2}$.\n\n2. First, simplify the numerator by combining like terms: $54y - 15y = 39y$. So numerator becomes $2y^2 + 39y + 10$.\n\n3. Simplify the denominator: $9 + 2 = 11$.\n\n4. Now the expression is $\frac{2y^2 + 39y + 10}{11}$.\n\n5. Since $11$ does not factor into any terms in the numerator, the expression cannot be simplified further.\n\n6. Final answer: $\frac{2y^2 + 39y + 10}{11}$.