Finite Math Examples

$\frac{a^{2} + a b + b^{2}}{a^{3} - b^{3}}$

Step 1

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = a$ and $b = b$ .

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

Step 2

Cancel the common factor of $a^{2} + a b + b^{2}$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$\frac{1}{a - b}$