Answer
$\dfrac{5x+8}{3}, \space x\ne0$
Work Step by Step
Note that $\dfrac{15x^2+24x}{3x^2}=\dfrac{3x(5x)+3x(8)}{3x\cdot x}$
Factor out $3x$ in the numerator.
$=\dfrac{3x(5x+8)}{3x\cdot x}$
Cancel common factor $3x$:
$=\dfrac{5x+8}{3}, \space x\ne0$
Hence, the lowest term is $\dfrac{5x+8}{3}, \space x\ne0$.
