Question

4. Add the rational expressions. Simplify your answer. *

(4x-3) / (x+5)(x-1)
5 / (x+5)(x-1)
4(x-1) / (x+5)
4x / (x+5)(x-1)

Answer 1

Explanation:

`(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}`