[tex] \frac{ {x}^{3} - {4x}^{2} - x + 4 }{ {x}^{2} - 5x + 4 } = \frac{ {x}^{2}(x - 4) - (x - 4) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)( {x}^{2} - 1) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)( {x}^{2} - {1}^{2}) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)(x + 1)(x - 1)}{(x - 4)(x - 1)} = x + 1 [/tex]