Answer:
[tex] \frac{ {x}^{3} - 1}{x - 1} \\ = \frac{ {x}^{3} - {1}^{3} }{x - 1} \\ = > but : {(x - 1)}^{3} = (x - 1)( {x}^{2} - 2x + 1) \\ \therefore \: = \frac{(x - 1)( {x}^{2} - 2x + 1) }{(x - 1)} \\ = {x}^{2} - 2x + 1 \\ = {(x - 1)}^{2} [/tex]
[tex] \frac{ {x}^{3} - 1 }{ x- 1} \\ = \frac{ {x}^{3} - 1 }{x - 1} \\ = \frac{( {x} - 1)( {x}^{2} + x + 1) }{x - 1} \\
= {x}^{2} +x+1[/tex]
