Question : What is the value of $\frac{(a^2+b^2)(a-b)-(a-b)^3}{a^2b-ab^2}?$
Option 1: $0$
Option 2: $1$
Option 3: $–1$
Option 4: $2$
Correct Answer: $2$
Solution :
Given: $\frac{(a^2+b^2)(a-b)-(a-b)^3}{a^2b-ab^2}$
= $\frac{(a-b)(a^2+b^2-(a-b)^2)}{ab(a-b)}$
= $\frac{a^2+b^2-a^2+2ab-b^2}{ab}$
= $\frac{2ab}{ab}$
= $2$
Hence, the correct answer is $2$.
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