[tex]\text{Area of rectangle} = \text{Length} \times \text{Width}\\\\\\\implies \text{Width} = \dfrac{\text{Area of reactangle}}{\text{Length}} = \dfrac{x^2 +8x +12}{x+6} = \dfrac{x^2 + 6x +2x +12}{x+6}\\\\\\\\ = \dfrac{x(x+6) +2(x+6)}{x+6}=\dfrac{(x+6)(x+2)}{x+6} = x+2[/tex]
