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

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

Evaluate

$$a+b$$

Short Solution Steps

Divide \frac{a^{2}+ab}{a^{2}-ab} by \frac{a^{2}+ab+b^{2}}{a^{3}-b^{3}} by multiplying \frac{a^{2}+ab}{a^{2}-ab} by the reciprocal of \frac{a^{2}+ab+b^{2}}{a^{3}-b^{3}}.

$$\frac{\left(a^{2}+ab\right)\left(a^{3}-b^{3}\right)}{\left(a^{2}-ab\right)\left(a^{2}+ab+b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out a\left(a-b\right)\left(a^{2}+ab+b^{2}\right) in both numerator and denominator.

$$a+b$$

Expand

$$a+b$$

Short Solution Steps

Divide \frac{a^{2}+ab}{a^{2}-ab} by \frac{a^{2}+ab+b^{2}}{a^{3}-b^{3}} by multiplying \frac{a^{2}+ab}{a^{2}-ab} by the reciprocal of \frac{a^{2}+ab+b^{2}}{a^{3}-b^{3}}.

$$\frac{\left(a^{2}+ab\right)\left(a^{3}-b^{3}\right)}{\left(a^{2}-ab\right)\left(a^{2}+ab+b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out a\left(a-b\right)\left(a^{2}+ab+b^{2}\right) in both numerator and denominator.

$$a+b$$