Solve for: (3x^2+7x+2)/(x+2)

Expression: $\left( 3{x}^{2}+7x+2 \right)\div\left( x+2 \right)$

Write the division as a fraction

$\frac{ 3{x}^{2}+7x+2 }{ x+2 }$

Write $7x$ as a sum

$\frac{ 3{x}^{2}+6x+x+2 }{ x+2 }$

Factor out $3x$ from the expression

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

Factor out $x+2$ from the expression

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

Cancel out the common factor $x+2$

$3x+1$