Question : Simplify the given expression.
$
\frac{432 \times 432+247 \times 247-432 \times 247}{432 \times 432 \times 432+247 \times 247 \times 247}
$
Option 1: $\frac{1}{259}$
Option 2: $\frac{1}{185}$
Option 3: $\frac{1}{679}$
Option 4: $\frac{1}{450}$
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Correct Answer: $\frac{1}{679}$
Solution :
$\frac{432^2+247^2-432 \times 247}{432^3+247^3}$
Using identity $x^3+y^3 = (x+y)(x^2+y^2-x \times y)$,
$\frac{432^2+247^2-432 \times 247}{(432+247)(432^2+247^2-432 \times 247)}$
$=\frac{1}{(432+247)}$
$= \frac{1}{679}$
Hence, the correct answer is $\frac{1}{679}$.
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