Question : What is the value of $\frac{(a^2+b^2)(a-b)-(a^3-b^3)}{a^2b-ab^2}?$
Option 1: 0
Option 2: 1
Option 3: –1
Option 4: 3
Answer (1)
8th Jan, 2024
Correct Answer: –1
Solution :
Given:
$\frac{(a^2+b^2)(a-b)-(a^3-b^3)}{a^2b-ab^2}$
= $\frac{(a^2+b^2)(a-b)-(a-b)(a^2+ab+b^2)}{a^2b-ab^2}$
= $\frac{(a-b)(a^2+b^2-a^2-ab-b^2)}{ab(a-b)}$
= $\frac{-ab}{ab}$
= $-1$
Hence, the correct answer is –1.
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