Step-by-step explanation:
[tex] \frac{4}{x + 5} + \frac{1}{ {x}^{2} + 4x - 5} \\ \\ = (x + 5)( {x}^{2} + 4x - 5) \\ = {x}^{3} + {4x}^{2} - 5x + {5x}^{2} + 20x - 25 \\ = {x}^{3} + {9x}^{2} + 15x - 25 \\ \\ = \frac{4( {x}^{2} + 4x - 5)}{ {x}^{3} + {9x}^{2} + 15x - 25} + \frac{1(x + 5)}{ {x}^{3} + {9x}^{2} + 15x - 25} \\ = \frac{ {4x}^{2} + 16x + 20 }{ {x}^{3} + {9x}^{2} + 15x - 25} + \frac{x + 5}{ {x}^{3} + {9x}^{2} + 15x - 25} \\ = \frac{ {4x}^{2} + 17x + 25 }{ {x}^{3} + {9x}^{2} + 15x - 25} [/tex]
