# Calculate: (2x^3-x^2-4x+3)/(x^2-2x+1)

## Expression: $\frac{ 2{x}^{3}-{x}^{2}-4x+3 }{ {x}^{2}-2x+1 }$

Write $-{x}^{2}$ as a sum

$\frac{ 2{x}^{3}-2{x}^{2}+{x}^{2}-4x+3 }{ {x}^{2}-2x+1 }$

Write $-4x$ as a difference

$\frac{ 2{x}^{3}-2{x}^{2}+{x}^{2}-x-3x+3 }{ {x}^{2}-2x+1 }$

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

$\frac{ 2{x}^{3}-2{x}^{2}+{x}^{2}-x-3x+3 }{ {\left( x-1 \right)}^{2} }$

Factor out $2{x}^{2}$ from the expression

$\frac{ 2{x}^{2} \times \left( x-1 \right)+{x}^{2}-x-3x+3 }{ {\left( x-1 \right)}^{2} }$

Factor out $x$ from the expression

$\frac{ 2{x}^{2} \times \left( x-1 \right)+x \times \left( x-1 \right)-3x+3 }{ {\left( x-1 \right)}^{2} }$

Factor out $-3$ from the expression

$\frac{ 2{x}^{2} \times \left( x-1 \right)+x \times \left( x-1 \right)-3\left( x-1 \right) }{ {\left( x-1 \right)}^{2} }$

Factor out $x-1$ from the expression

$\frac{ \left( x-1 \right) \times \left( 2{x}^{2}+x-3 \right) }{ {\left( x-1 \right)}^{2} }$

Cancel out the common factor $x-1$

$\frac{ 2{x}^{2}+x-3 }{ x-1 }$

Write $x$ as a difference

$\frac{ 2{x}^{2}+3x-2x-3 }{ x-1 }$

Factor out $x$ from the expression

$\frac{ x \times \left( 2x+3 \right)-2x-3 }{ x-1 }$

Factor out the negative sign from the expression

$\frac{ x \times \left( 2x+3 \right)-\left( 2x+3 \right) }{ x-1 }$

Factor out $2x+3$ from the expression

$\frac{ \left( 2x+3 \right) \times \left( x-1 \right) }{ x-1 }$

Cancel out the common factor $x-1$

$2x+3$

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