What is the value of frac{(a^{2}+b^{2})(a-b)- | vedclass

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(D) Given expression: $\frac{(a^{2}+b^{2})(a-b)-(a-b)^{3}}{a^{2}b-ab^{2}}$Factor out $(a-b)$ from the numerator and $ab$ from the denominator:$= \frac

Vedclass · Accepted Answer

$2$

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(D) Given expression: $\frac{(a^{2}+b^{2})(a-b)-(a-b)^{3}}{a^{2}b-ab^{2}}$Factor out $(a-b)$ from the numerator and $ab$ from the denominator:$= \frac{(a-b)[(a^{2}+b^{2})-(a-b)^{2}]}{ab(a-b)}$Cancel $(a-b)$ from the numerator and denominator:$= \frac{(a^{2}+b^{2})-(a^{2}-2ab+b^{2})}{ab}$Simplify the numerator:$= \frac{a^{2}+b^{2}-a^{2}+2ab-b^{2}}{ab}$$= \frac{2ab}{ab}$$= 2$

What is the value of $\frac{(a^{2}+b^{2})(a-b)-(a-b)^{3}}{a^{2}b-ab^{2}}$?

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