For all values of $x$ for which the expression is defined, simplify $\dfrac{7x^{2} + 14x}{2x + 4}$.

Factor numerator and denominator separately. - Numerator: $7x^{2} + 14x = 7x(x + 2)$. - Denominator: $2x + 4 = 2(x + 2)$. So the expression becomes $\dfrac{7x(x + 2)}{2(x + 2)}$. The $(x + 2)$ factor cancels (valid where $x \ne -2$), leaving $\dfrac{7x}{2}$. The trap B ($\dfrac{7x+14}{2}$) is what you get if you cancel one $x$ in the numerator with $\dfrac{1}{2x+4}$ illegally — you can't cancel terms across a sum.