The given expression is:

$\frac{(876 + 346)^2 + (874 - 346)^2}{(876 \times 876 + 346 \times 346)}$

Step 1: Simplify the numerator

First term: $(876 + 346)^2$

$876 + 346 = 1222$ $1222^2 = 1490884$

Second term: $(874 - 346)^2$

$874 - 346 = 528$ $528^2 = 278784$

Now, the numerator becomes: $1490884 + 278784 = 1769668$

Step 2: Simplify the denominator

$876 \times 876 = 767376$ $346 \times 346 = 119716$

Now, the denominator becomes: $767376 + 119716 = 887092$

Step 3: Compute the final value

Now, divide the numerator by the denominator: $\frac{1769668}{887092} \approx 1.995$

This rounds to approximately $2$.

Answer:

The correct answer is $\boxed{2}$.

Would you like further details on any of the steps or have any other questions?

5 Related Questions:

1. How do you square a binomial expression like $(a + b)^2$?
2. What is the general approach to solving such algebraic fractions?
3. Can this expression be solved using factoring techniques?
4. How can we use approximation techniques for large numbers in such problems?
5. What are the steps to simplify complex numerators or denominators?

Tip:

Always double-check your arithmetic, especially when working with large numbers, to avoid simple calculation errors!