Solve frac{a^{2}-ab}{7a^{2}+7ab}+a^3-b^3/a^2-b^2

$$\frac { a ^ { 2 } - a b } { 7 a ^ { 2 } + 7 a b } + \frac { a ^ { 3 } - b ^ { 3 } } { a ^ { 2 } - b ^ { 2 } }$$

Evaluate

$$\frac{7a^{2}+7ab+a+7b^{2}-b}{7\left(a+b\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{7a^{2}+7ab}.

$$\frac{a\left(a-b\right)}{7a\left(a+b\right)}+\frac{a^{3}-b^{3}}{a^{2}-b^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-b}{7\left(a+b\right)}+\frac{a^{3}-b^{3}}{a^{2}-b^{2}}$$

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

$$\frac{a-b}{7\left(a+b\right)}+\frac{\left(a-b\right)\left(a^{2}+ab+b^{2}\right)}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a-b in both numerator and denominator.

$$\frac{a-b}{7\left(a+b\right)}+\frac{a^{2}+ab+b^{2}}{a+b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(a+b\right) and a+b is 7\left(a+b\right). Multiply \frac{a^{2}+ab+b^{2}}{a+b} times \frac{7}{7}.

$$\frac{a-b}{7\left(a+b\right)}+\frac{7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)}$$

Since \frac{a-b}{7\left(a+b\right)} and \frac{7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)} have the same denominator, add them by adding their numerators.

$$\frac{a-b+7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)}$$

Do the multiplications in a-b+7\left(a^{2}+ab+b^{2}\right).

$$\frac{a-b+7a^{2}+7ab+7b^{2}}{7\left(a+b\right)}$$

Expand 7\left(a+b\right).

$$\frac{a-b+7a^{2}+7ab+7b^{2}}{7a+7b}$$

Expand

$$\frac{7a^{2}+7ab+a+7b^{2}-b}{7\left(a+b\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{7a^{2}+7ab}.

$$\frac{a\left(a-b\right)}{7a\left(a+b\right)}+\frac{a^{3}-b^{3}}{a^{2}-b^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-b}{7\left(a+b\right)}+\frac{a^{3}-b^{3}}{a^{2}-b^{2}}$$

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

$$\frac{a-b}{7\left(a+b\right)}+\frac{\left(a-b\right)\left(a^{2}+ab+b^{2}\right)}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a-b in both numerator and denominator.

$$\frac{a-b}{7\left(a+b\right)}+\frac{a^{2}+ab+b^{2}}{a+b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(a+b\right) and a+b is 7\left(a+b\right). Multiply \frac{a^{2}+ab+b^{2}}{a+b} times \frac{7}{7}.

$$\frac{a-b}{7\left(a+b\right)}+\frac{7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)}$$

Since \frac{a-b}{7\left(a+b\right)} and \frac{7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)} have the same denominator, add them by adding their numerators.

$$\frac{a-b+7\left(a^{2}+ab+b^{2}\right)}{7\left(a+b\right)}$$

Do the multiplications in a-b+7\left(a^{2}+ab+b^{2}\right).

$$\frac{a-b+7a^{2}+7ab+7b^{2}}{7\left(a+b\right)}$$

Expand 7\left(a+b\right).

$$\frac{a-b+7a^{2}+7ab+7b^{2}}{7a+7b}$$