Question : The value of $\frac{(m^2+n^2)(m-n)-(m-n)^3}{(m^2 n-m n^2)}$ is:
Option 1: $m + n$
Option 2: $m - n$
Option 3: $2$
Option 4: $\frac{m}{n}$
Answer (1)
21st Jan, 2024
Correct Answer: $2$
Solution :
$\frac{(m^2+n^2)(m-n)-(m-n)^3}{(m^2 n-m n^2)}$
= $\frac{(m-n)[(m^2+n^2)-(m-n)^2]}{mn(m-n)}$
= $\frac{[m^2+n^2-m^2-n^2+2mn]}{mn}$
= $\frac{2mn}{mn}$
= $2$
Hence, the correct answer is 2.
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