Solve frac{a^{3}}{a^{2}+ab+b^2}-b^3/a^2+ab+b^2

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

Evaluate

$$a-b$$

Short Solution Steps

Since \frac{a^{3}}{a^{2}+ab+b^{2}} and \frac{b^{3}}{a^{2}+ab+b^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Factor the expressions that are not already factored in \frac{a^{3}-b^{3}}{a^{2}+ab+b^{2}}.

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

Cancel out a^{2}+ab+b^{2} in both numerator and denominator.

$$a-b$$

Factor

$$a-b$$