Calculate: (3x^2-22x+7)/(3x-1)

Expression: $\frac{ 3{x}^{2}-22x+7 }{ 3x-1 }$

Write $-22x$ as a difference

$\frac{ 3{x}^{2}-x-21x+7 }{ 3x-1 }$

Factor out $x$ from the expression

$\frac{ x \times \left( 3x-1 \right)-21x+7 }{ 3x-1 }$

Factor out $-7$ from the expression

$\frac{ x \times \left( 3x-1 \right)-7\left( 3x-1 \right) }{ 3x-1 }$

Factor out $3x-1$ from the expression

$\frac{ \left( 3x-1 \right) \times \left( x-7 \right) }{ 3x-1 }$

Cancel out the common factor $3x-1$

$x-7$