Use the sum-of-cubes factorization: Compute [(8.73)^3 + (4.27)^3] / [(8.73)^2 − (8.73)(4.27) + (4.27)^2].

Introduction / Context:
This is a direct application of the identity a^3 + b^3 = (a + b)(a^2 − ab + b^2). Since the denominator equals a^2 − ab + b^2, the quotient collapses to a + b. No heavy computation is required beyond adding the two bases.

Given Data / Assumptions:

• a = 8.73, b = 4.27.
• We compute (a^3 + b^3) / (a^2 − ab + b^2).
• Assume exact arithmetic (identity holds for all real a, b).

Concept / Approach:
Recognize the pattern and reduce: (a^3 + b^3)/(a^2 − ab + b^2) = a + b.

Step-by-Step Solution:

Verification / Alternative check:
Multiplying (a + b)(a^2 − ab + b^2) re-expands to a^3 + b^3, confirming the simplification.

Why Other Options Are Wrong:
11 and 12 are near-sum guesses; 11/7 is unrelated; “None of these” is invalid because 13 is correct by identity.

Common Pitfalls:
Attempting to cube decimals directly (time-consuming) instead of using the identity; misreading the denominator as a^2 + ab + b^2 (that is for a^3 − b^3).

Final Answer:
13