Calculate: (x^3-1)\div(x-1)

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Expression: $\left( {x}^{3}-1 \right)\div\left( x-1 \right)$

Write the division as a fraction

$\frac{ {x}^{3}-1 }{ x-1 }$

Use ${a}^{3}-{b}^{3}=\left( a-b \right)\left( {a}^{2}+ab+{b}^{2} \right)$ to factor the expression

$\frac{ \left( x-1 \right) \times \left( {x}^{2}+x+1 \right) }{ x-1 }$

Cancel out the common factor $x-1$

${x}^{2}+x+1$

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