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