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

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

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

$$\frac{a^{2}+ab}{ab+b^{2}}\times \frac{a}{b}$$

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

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

$$\frac{a^{2}}{b^{2}}$$

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

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

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

$$\frac{a^{2}+ab}{ab+b^{2}}\times \frac{a}{b}$$

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

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

$$\frac{a^{2}}{b^{2}}$$