$$\frac{\left(n-2\right)\left(2n+1\right)}{\left(n+1\right)\left(2n+1\right)}\times \frac{n^{2}-1}{n^{2}-4}$$

$$\frac{n-2}{n+1}\times \frac{n^{2}-1}{n^{2}-4}$$

$$\frac{\left(n-2\right)\left(n^{2}-1\right)}{\left(n+1\right)\left(n^{2}-4\right)}$$

$$\frac{\left(n-2\right)\left(n-1\right)\left(n+1\right)}{\left(n-2\right)\left(n+1\right)\left(n+2\right)}$$

$$\frac{n-1}{n+2}$$

$$\frac{\left(n-2\right)\left(2n+1\right)}{\left(n+1\right)\left(2n+1\right)}\times \frac{n^{2}-1}{n^{2}-4}$$

$$\frac{n-2}{n+1}\times \frac{n^{2}-1}{n^{2}-4}$$

$$\frac{\left(n-2\right)\left(n^{2}-1\right)}{\left(n+1\right)\left(n^{2}-4\right)}$$

$$\frac{\left(n-2\right)\left(n-1\right)\left(n+1\right)}{\left(n-2\right)\left(n+1\right)\left(n+2\right)}$$

$$\frac{n-1}{n+2}$$