Question

Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.

Answer 1

Answer:

  4u²

Step-by-step explanation:

  $\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}$

Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.