Question

The lowest form of the$\frac{a^2-b^2}{a^3-b^3}$ is___

• A. $\frac{a+b}{a^2-ab+b^2}$
• B. $\frac{a+b}{a^2+ab+b^2}$
• C. $\frac{a-b}{a^2+ab+b^2}$
• D. $\frac{a-b}{a^2-ab+b^2}$

Answer 1

The correct option is B

$\frac{a+b}{a^2+ab+b^2}$

Given fraction is $\frac{a^2-b^2}{a^3-b^3}$.

$(a^2-b^2)canbewrittenas(a+b)\times (a-b)$

$Similarly(a^3-b^3)=(a-b)\times (a^2+ab+b^2)$

$⟹$ $\frac{a^2-b^2}{a^3-b^3}=\frac{(a+b)\times (a-b)}{(a-b)\times (a^2+ab+b^2)}$

= $\frac{a+b}{a^2+ab+b^2}$