\( \Large \frac{ \left(m-n\right)^{3}+ \left(n-r\right)^{3}+ \left(r-m\right)^{3} }{6 \left(m-n\right) \left(n-r\right) \left(r-m\right) }=? \)

A) \( \Large \frac{1}{2} \)

B) \( \Large \frac{1}{3} \)

C) \( \Large \frac{1}{4} \)

D) \( \Large \frac{1}{6} \)

Correct answer:
A) \( \Large \frac{1}{2} \)

Description for Correct answer:
Let, \( \Large \left(m-n\right)=a, \left(n-r\right)=b, \left(r-m\right)=c \)

we get

\( \Large a+b+c = 0 \)

Therefore, \( \Large a^{3}+b^{3}+c^{3} = 3abc \)

Therefore, Given expression \( \Large \frac{a^{3}+b^{3}+c^{3}}{6 abc} = \frac{3abc}{6abc}=\frac{1}{2} \)

Please provide the error details in above question

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