Answer
$\dfrac{x}{3}, \space x\ne-2$.
Work Step by Step
Note that $\dfrac{4x^2+8x}{12x+24}=\dfrac{4x^2+2(4x)}{12x+12(2)}$
Factor out $4x$ in the numerator and $12$ in the denominator.
$=\dfrac{4x(x+2)}{12(x+2)}$
$=\dfrac{4x(x+2)}{4(3)(x+2)}$
Cancel common factors $x+2$ and $3$.
$=\dfrac{x}{3}, \space x\ne-2$
Hence, the lowest term is $\dfrac{x}{3}, \space x\ne-2$.
