# Solution {-}
Factor spectral density function $S(s)$:


```python
from sympy import symbols, factor

s, sigma, beta, K = symbols('s sigma beta K')

Sx = 1/(s + K)*1/(-s + K)*(2*sigma**2*beta)/(-s**2 + beta**2)
Sx
```




$\displaystyle \frac{2 \beta \sigma^{2}}{\left(K - s\right) \left(K + s\right) \left(\beta^{2} - s^{2}\right)}$




```python
factor(Sx, s)
```




$\displaystyle \frac{2 \beta \sigma^{2}}{\left(- K + s\right) \left(K + s\right) \left(- \beta + s\right) \left(\beta + s\right)}$



287abc8d6193cee3f8225d84ac38bc9aeb35cc00
ipynb
Jupyter Notebook
Problem 3.3.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-07T09:36:36.000Z
2021-09-07T09:36:36.000Z
Problem 3.3.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
Problem 3.3.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-20T18:48:20.000Z
2021-09-20T18:48:20.000Z
Qwen/Qwen-72B
1. YES
2. YES