The lowest form of the a2-b2-a3-b3 is

The correct option is C a+b/a^2+ab+b^2 Given fraction is a^2 b^2/a^3 b^3. (a^2 b^2) can be written as (a+b) × (a b) Similarly (a^3 b^3) = (a b) × (a^ ...

The lowest fo...

Question

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

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

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

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

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

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Solution

The correct option is C
$\frac{a + b}{a^{2} + a b + b^{2}}$

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

$(a^{2} - b^{2}) c a n b e w r i t t e n a s (a + b) \times (a - b)$

$S i m i l a r l y (a^{3} - b^{3}) = (a - b) \times (a^{2} + a b + b^{2})$

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

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

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Similar questions

The shortest form of $\frac{(a^{3} + b^{3})}{(a^{2} - a b + b^{2})}$ is ___.

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The lowest form of thea2−b2a3−b3 is___

The correct option is C a+ba2+ab+b2 Given fraction is a2−b2a3−b3. (a2−b2) can be written as (a+b)×(a−b) Similarly (a3−b3) = (a−b)×(a2+ab+b2) ⟹ a2−b2a3−b3 =(a+b)×(a−b)(a−b)×(a2+ab+b2) = a+ba2+ab+b2

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