$$\frac{\left(x-6\right)\left(x-5\right)}{\left(x-5\right)\left(x+2\right)}\times \frac{5x+10}{x^{2}-8x+12}$$

$$\frac{x-6}{x+2}\times \frac{5x+10}{x^{2}-8x+12}$$

$$\frac{\left(x-6\right)\left(5x+10\right)}{\left(x+2\right)\left(x^{2}-8x+12\right)}$$

$$\frac{5\left(x-6\right)\left(x+2\right)}{\left(x-6\right)\left(x-2\right)\left(x+2\right)}$$

$$\frac{5}{x-2}$$

$$\frac{\left(x-6\right)\left(x-5\right)}{\left(x-5\right)\left(x+2\right)}\times \frac{5x+10}{x^{2}-8x+12}$$

$$\frac{x-6}{x+2}\times \frac{5x+10}{x^{2}-8x+12}$$

$$\frac{\left(x-6\right)\left(5x+10\right)}{\left(x+2\right)\left(x^{2}-8x+12\right)}$$

$$\frac{5\left(x-6\right)\left(x+2\right)}{\left(x-6\right)\left(x-2\right)\left(x+2\right)}$$

$$\frac{5}{x-2}$$