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