Question

Forma ireductibilă a fractiei

Answer 1

$\frac{ {x}^{3} - 4 {x}^{2} - x + 4}{ {x}^{2} - 5x + 4 } = \frac{ {x}^{2}(x - 4) - (x - 4) }{ {x}^{2} - x - 4x + 4 }$

$= \frac{(x - 4)( {x}^{2} - 1)}{x(x - 1) - 4(x - 1)} = \frac{(x - 4)(x - 1)(x + 1)}{(x - 4)(x - 1)} = x + 1$

Answer 2

$\frac{ {x}^{3} - {4x}^{2} - x + 4 }{ {x}^{2} - 5x + 4 } = \frac{ {x}^{2}(x - 4) - (x - 4) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)( {x}^{2} - 1) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)( {x}^{2} - {1}^{2}) }{ {x}^{2} - 5x + 4 } = \frac{(x - 4)(x + 1)(x - 1)}{(x - 4)(x - 1)} = x + 1$