$$\frac{x^{2}-8x+15}{x^{2}+31}\times \frac{x^{2}-8x-9}{x^{2}+2x-15}$$

$$\frac{\left(x^{2}-8x+15\right)\left(x^{2}-8x-9\right)}{\left(x^{2}+31\right)\left(x^{2}+2x-15\right)}$$

$$\frac{\left(x-9\right)\left(x-5\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x+5\right)\left(x^{2}+31\right)}$$

$$\frac{\left(x-9\right)\left(x-5\right)\left(x+1\right)}{\left(x+5\right)\left(x^{2}+31\right)}$$

$$\frac{x^{3}-13x^{2}+31x+45}{x^{3}+5x^{2}+31x+155}$$

$$\frac{x^{2}-8x+15}{x^{2}+31}\times \frac{x^{2}-8x-9}{x^{2}+2x-15}$$

$$\frac{\left(x^{2}-8x+15\right)\left(x^{2}-8x-9\right)}{\left(x^{2}+31\right)\left(x^{2}+2x-15\right)}$$

$$\frac{\left(x-9\right)\left(x-5\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x+5\right)\left(x^{2}+31\right)}$$

$$\frac{\left(x-9\right)\left(x-5\right)\left(x+1\right)}{\left(x+5\right)\left(x^{2}+31\right)}$$

$$\frac{x^{3}-13x^{2}+31x+45}{x^{3}+5x^{2}+31x+155}$$