1. The problem is to simplify the expression $$\frac{48 \times 18}{(18 \times 46) + (36 \times 92)}$$. 2. First, calculate the numerator: $$48 \times 18 = 864$$. 3. Next, calculate each term in the denominator: - $$18 \times 46 = 828$$ - $$36 \times 92 = 3312$$ 4. Sum the terms in the denominator: $$828 + 3312 = 4140$$. 5. Now we have the fraction: $$\frac{864}{4140}$$. 6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 864 and 4140 is 12. 7. Divide numerator and denominator by 12: $$\frac{864 \div 12}{4140 \div 12} = \frac{72}{345}$$. 8. Further simplify by dividing numerator and denominator by 3: $$\frac{72 \div 3}{345 \div 3} = \frac{24}{115}$$. 9. Thus, the simplified value of the expression is $$\frac{24}{115}$$.