Simplify the given expression.
​$$\frac{432 \times 432 + 247 \times 247 - 432 \times 247}{432 \times 432 \times 432 + 247 \times 247 \times 247}$$​​

Correct option is C

Given:

$$\frac{432\times432+247\times247-432\times247}{432\times432\times432 +247\times247\times247}$$​

Formula Used:

a³ + b³ = (a + b)(a² − ab + b²)

Solution:

a = 432 , b = 247 

then,

 $$\begin{aligned}&\Rightarrow \frac{432 \times 432 + 247 \times 247 - 432 \times 247}{432 \times 432 + 247 \times 247 + 432 \times 247} \\[6pt]&\Rightarrow \frac{(432)^2 + (247)^2 - 432 \times 247}{(432)^3 + (247)^3} \\[6pt]&\Rightarrow \frac{[(432)^2 + (247)^2 - 432 \times 247]}{[(432) + (247)](432^2 + 247^2 - 432 \times 247)} \\[6pt]&\Rightarrow \frac{1}{432 + 247} \\[6pt]&\Rightarrow \frac{1}{679}\end{aligned}$$​
​